Add <math><mstyle displaystyle="true"><mn>2</mn><mi>x</mi></mstyle></math> to both sides of the equation.

Replace all occurrences of <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> in <math><mstyle displaystyle="true"><mn>2</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>4</mn><mi>x</mi><mo>-</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>3</mn></mstyle></math> with <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn><mo>+</mo><mn>2</mn><mi>x</mi></mstyle></math> .

Simplify the left side.

Simplify <math><mstyle displaystyle="true"><mn>2</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>4</mn><mi>x</mi><mo>-</mo><mrow><mo>(</mo><mo>-</mo><mn>4</mn><mo>+</mo><mn>2</mn><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Simplify each term.

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>2</mn><mi>x</mi></mstyle></math> from <math><mstyle displaystyle="true"><mn>4</mn><mi>x</mi></mstyle></math> .

Move all terms to the left side of the equation and simplify.

Add <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> to both sides of the equation.

Add <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Use the quadratic formula to find the solutions.

Substitute the values <math><mstyle displaystyle="true"><mi>a</mi><mo>=</mo><mn>2</mn></mstyle></math> , <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mn>2</mn></mstyle></math> , and <math><mstyle displaystyle="true"><mi>c</mi><mo>=</mo><mn>7</mn></mstyle></math> into the quadratic formula and solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Simplify.

Simplify the numerator.

Raise <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>8</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>56</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>52</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>52</mn><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>52</mn><mo>)</mo></mrow></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn></msqrt><mo>⋅</mo><msqrt><mn>52</mn></msqrt></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><mi>i</mi></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>52</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>13</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>52</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

Move <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>i</mi></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>2</mn><mo>±</mo><mn>2</mn><mi>i</mi><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Simplify the expression to solve for the <math><mstyle displaystyle="true"><mo>+</mo></mstyle></math> portion of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> .

Simplify the numerator.

Raise <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>8</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>56</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>52</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>52</mn><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>52</mn><mo>)</mo></mrow></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn></msqrt><mo>⋅</mo><msqrt><mn>52</mn></msqrt></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><mi>i</mi></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>52</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>13</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>52</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

Move <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>i</mi></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>2</mn><mo>±</mo><mn>2</mn><mi>i</mi><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Change the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to <math><mstyle displaystyle="true"><mo>+</mo></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mi>i</mi><msqrt><mn>13</mn></msqrt></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mo>-</mo><mrow><mo>(</mo><mo>-</mo><mi>i</mi><msqrt><mn>13</mn></msqrt><mo>)</mo></mrow></mstyle></math> .

Move the negative in front of the fraction.

Simplify the expression to solve for the <math><mstyle displaystyle="true"><mo>-</mo></mstyle></math> portion of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> .

Simplify the numerator.

Raise <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>8</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>56</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>52</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>52</mn><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>52</mn><mo>)</mo></mrow></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn></msqrt><mo>⋅</mo><msqrt><mn>52</mn></msqrt></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><mi>i</mi></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>52</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>13</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>52</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

Move <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>i</mi></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>2</mn><mo>±</mo><mn>2</mn><mi>i</mi><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Change the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to <math><mstyle displaystyle="true"><mo>-</mo></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mi>i</mi><msqrt><mn>13</mn></msqrt></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mo>-</mo><mrow><mo>(</mo><mi>i</mi><msqrt><mn>13</mn></msqrt><mo>)</mo></mrow></mstyle></math> .

Move the negative in front of the fraction.

The final answer is the combination of both solutions.

Replace all occurrences of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> in <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mo>-</mo><mn>4</mn><mo>+</mo><mn>2</mn><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>1</mn><mo>-</mo><mi>i</mi><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Simplify the right side.

Simplify <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn><mo>+</mo><mn>2</mn><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>1</mn><mo>-</mo><mi>i</mi><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> .

Simplify each term.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Move the leading negative in <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>1</mn><mo>-</mo><mi>i</mi><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> into the numerator.

Cancel the common factor.

Rewrite the expression.

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mrow><mo>(</mo><mo>-</mo><mi>i</mi><msqrt><mn>13</mn></msqrt><mo>)</mo></mrow></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><msqrt><mn>13</mn></msqrt></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> from <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> .

Replace all occurrences of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> in <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mo>-</mo><mn>4</mn><mo>+</mo><mn>2</mn><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>1</mn><mo>+</mo><mi>i</mi><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Simplify the right side.

Simplify <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn><mo>+</mo><mn>2</mn><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>1</mn><mo>+</mo><mi>i</mi><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> .

Simplify each term.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Move the leading negative in <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>1</mn><mo>+</mo><mi>i</mi><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> into the numerator.

Cancel the common factor.

Rewrite the expression.

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> from <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> .

List all of the solutions.

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