Solve for x 2/3x^2=24

$\frac{2}{3} x^{2} = 24$

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} (\frac{2}{3} x^{2}) = \frac{3}{2} \cdot 24$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} (\frac{2}{3} x^{2})$ .

Combine $\frac{2}{3}$ and $x^{2}$ .

$\frac{3}{2} \cdot \frac{2 x^{2}}{3} = \frac{3}{2} \cdot 24$

Combine.

$\frac{3 (2 x^{2})}{2 \cdot 3} = \frac{3}{2} \cdot 24$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (2 x^{2})}{2 \cdot 3} = \frac{3}{2} \cdot 24$

Rewrite the expression.

$\frac{2 x^{2}}{2} = \frac{3}{2} \cdot 24$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{3}{2} \cdot 24$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{3}{2} \cdot 24$

Simplify the right side.

Simplify $\frac{3}{2} \cdot 24$ .

Cancel the common factor of $2$ .

Factor $2$ out of $24$ .

$x^{2} = \frac{3}{2} \cdot (2 (12))$

Cancel the common factor.

$x^{2} = \frac{3}{2} \cdot (2 \cdot 12)$

Rewrite the expression.

$x^{2} = 3 \cdot 12$

Multiply $3$ by $12$ .

$x^{2} = 36$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{36}$

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

$x = \pm \sqrt{6^{2}}$

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

$x = \pm 6$

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

First, use the positive value of the $\pm$ to find the first solution.

$x = 6$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 6$

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

$x = 6, - 6$