Take the square root of each side of the equation to set up the solution for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math>

Remove the perfect root factor <math><mstyle displaystyle="true"><mn>5</mn><mi>x</mi><mo>-</mo><mn>6</mn></mstyle></math> under the radical to solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>64</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>8</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical, assuming positive real numbers.

First, use the positive value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the first solution.

Move all terms not containing <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> to the right side of the equation.

Add <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> to both sides of the equation.

Add <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Divide each term by <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>5</mn><mi>x</mi><mo>=</mo><mn>14</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Next, use the negative value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the second solution.

Move all terms not containing <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> to the right side of the equation.

Add <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> to both sides of the equation.

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>8</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Divide each term by <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>5</mn><mi>x</mi><mo>=</mo><mo>-</mo><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Move the negative in front of the fraction.

The complete solution is the result of both the positive and negative portions of the solution.

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