Solve for x (2x^2)/3=dg

$\frac{2 x^{2}}{3} = d g$

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

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} \cdot \frac{2 x^{2}}{3}$ .

Combine.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 x^{2}}{2} = \frac{3}{2} (d g)$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{3}{2} (d g)$

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

$x^{2} = \frac{3}{2} (d g)$

Simplify the right side.

Simplify $\frac{3}{2} (d g)$ .

Multiply $\frac{3}{2} (d g)$ .

Combine $d$ and $\frac{3}{2}$ .

$x^{2} = \frac{d \cdot 3}{2} g$

Combine $\frac{d \cdot 3}{2}$ and $g$ .

$x^{2} = \frac{d \cdot 3 g}{2}$

Move $3$ to the left of $d$ .

$x^{2} = \frac{3 d g}{2}$

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

$x = \pm \sqrt{\frac{3 d g}{2}}$

Simplify $\pm \sqrt{\frac{3 d g}{2}}$ .

Rewrite $\sqrt{\frac{3 d g}{2}}$ as $\frac{\sqrt{3 d g}}{\sqrt{2}}$ .

$x = \pm \frac{\sqrt{3 d g}}{\sqrt{2}}$

Multiply $\frac{\sqrt{3 d g}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$x = \pm \frac{\sqrt{3 d g}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{3 d g}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$x = \pm \frac{\sqrt{3 d g} \sqrt{2}}{\sqrt{2} \sqrt{2}}$

Raise $\sqrt{2}$ to the power of $1$ .

$x = \pm \frac{\sqrt{3 d g} \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}}$

Raise $\sqrt{2}$ to the power of $1$ .

$x = \pm \frac{\sqrt{3 d g} \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = \pm \frac{\sqrt{3 d g} \sqrt{2}}{{\sqrt{2}}^{1 + 1}}$

Add $1$ and $1$ .

$x = \pm \frac{\sqrt{3 d g} \sqrt{2}}{{\sqrt{2}}^{2}}$

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$x = \pm \frac{\sqrt{3 d g} \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x = \pm \frac{\sqrt{3 d g} \sqrt{2}}{2^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$x = \pm \frac{\sqrt{3 d g} \sqrt{2}}{2^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = \pm \frac{\sqrt{3 d g} \sqrt{2}}{2^{\frac{2}{2}}}$

Rewrite the expression.

$x = \pm \frac{\sqrt{3 d g} \sqrt{2}}{2^{1}}$

Evaluate the exponent.

$x = \pm \frac{\sqrt{3 d g} \sqrt{2}}{2}$

Simplify the numerator.

Combine using the product rule for radicals.

$x = \pm \frac{\sqrt{3 d g \cdot 2}}{2}$

Multiply $2$ by $3$ .

$x = \pm \frac{\sqrt{6 d g}}{2}$

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.

$x = \frac{\sqrt{6 d g}}{2}$

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

$x = - \frac{\sqrt{6 d g}}{2}$

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

$x = \frac{\sqrt{6 d g}}{2}$

$x = - \frac{\sqrt{6 d g}}{2}$

$x = \frac{\sqrt{6 d g}}{2}$

$x = - \frac{\sqrt{6 d g}}{2}$

Solve for x (2x^2)/3=dg

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