Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

Rewrite the equation as <math><mstyle displaystyle="true"><mi>x</mi><mo>⋅</mo><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow><mo>=</mo><mn>5</mn><mo>⋅</mo><mn>6</mn></mstyle></math> .

Simplify <math><mstyle displaystyle="true"><mi>x</mi><mo>⋅</mo><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow></mstyle></math> .

Apply the distributive property.

Simplify the expression.

Multiply <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Move <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Move <math><mstyle displaystyle="true"><mn>30</mn></mstyle></math> to the left side of the equation by subtracting it from both sides.

Use the quadratic formula to find the solutions.

Substitute the values <math><mstyle displaystyle="true"><mi>a</mi><mo>=</mo><mn>1</mn></mstyle></math> , <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mn>3</mn></mstyle></math> , and <math><mstyle displaystyle="true"><mi>c</mi><mo>=</mo><mo>-</mo><mn>30</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>3</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>30</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>30</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>120</mn></mstyle></math> .

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

The final answer is the combination of both solutions.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

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