Solve for A 5h^3=bA^2-G

$5 h^{3} = b A^{2} - G$

Rewrite the equation as $b A^{2} - G = 5 h^{3}$ .

$b A^{2} - G = 5 h^{3}$

Add $G$ to both sides of the equation.

$b A^{2} = 5 h^{3} + G$

Divide each term in $b A^{2} = 5 h^{3} + G$ by $b$ and simplify.

Divide each term in $b A^{2} = 5 h^{3} + G$ by $b$ .

$\frac{b A^{2}}{b} = \frac{5 h^{3}}{b} + \frac{G}{b}$

Simplify the left side.

Cancel the common factor of $b$ .

Cancel the common factor.

$\frac{b A^{2}}{b} = \frac{5 h^{3}}{b} + \frac{G}{b}$

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

$A^{2} = \frac{5 h^{3}}{b} + \frac{G}{b}$

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

$A = \pm \sqrt{\frac{5 h^{3}}{b} + \frac{G}{b}}$

Simplify $\pm \sqrt{\frac{5 h^{3}}{b} + \frac{G}{b}}$ .

Combine the numerators over the common denominator.

$A = \pm \sqrt{\frac{5 h^{3} + G}{b}}$

Rewrite $\sqrt{\frac{5 h^{3} + G}{b}}$ as $\frac{\sqrt{5 h^{3} + G}}{\sqrt{b}}$ .

$A = \pm \frac{\sqrt{5 h^{3} + G}}{\sqrt{b}}$

Multiply $\frac{\sqrt{5 h^{3} + G}}{\sqrt{b}}$ by $\frac{\sqrt{b}}{\sqrt{b}}$ .

$A = \pm \frac{\sqrt{5 h^{3} + G}}{\sqrt{b}} \cdot \frac{\sqrt{b}}{\sqrt{b}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{5 h^{3} + G}}{\sqrt{b}}$ by $\frac{\sqrt{b}}{\sqrt{b}}$ .

$A = \pm \frac{\sqrt{5 h^{3} + G} \sqrt{b}}{\sqrt{b} \sqrt{b}}$

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

$A = \pm \frac{\sqrt{5 h^{3} + G} \sqrt{b}}{{\sqrt{b}}^{1} \sqrt{b}}$

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

$A = \pm \frac{\sqrt{5 h^{3} + G} \sqrt{b}}{{\sqrt{b}}^{1} {\sqrt{b}}^{1}}$

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

$A = \pm \frac{\sqrt{5 h^{3} + G} \sqrt{b}}{{\sqrt{b}}^{1 + 1}}$

Add $1$ and $1$ .

$A = \pm \frac{\sqrt{5 h^{3} + G} \sqrt{b}}{{\sqrt{b}}^{2}}$

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

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

$A = \pm \frac{\sqrt{5 h^{3} + G} \sqrt{b}}{{(b^{\frac{1}{2}})}^{2}}$

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

$A = \pm \frac{\sqrt{5 h^{3} + G} \sqrt{b}}{b^{\frac{1}{2} \cdot 2}}$

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

$A = \pm \frac{\sqrt{5 h^{3} + G} \sqrt{b}}{b^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$A = \pm \frac{\sqrt{5 h^{3} + G} \sqrt{b}}{b^{\frac{2}{2}}}$

Rewrite the expression.

$A = \pm \frac{\sqrt{5 h^{3} + G} \sqrt{b}}{b^{1}}$

Simplify.

$A = \pm \frac{\sqrt{5 h^{3} + G} \sqrt{b}}{b}$

Combine using the product rule for radicals.

$A = \pm \frac{\sqrt{(5 h^{3} + G) b}}{b}$

Reorder factors in $\pm \frac{\sqrt{(5 h^{3} + G) b}}{b}$ .

$A = \pm \frac{\sqrt{b (5 h^{3} + G)}}{b}$

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.

$A = \frac{\sqrt{b (5 h^{3} + G)}}{b}$

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

$A = - \frac{\sqrt{b (5 h^{3} + G)}}{b}$

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

$A = \frac{\sqrt{b (5 h^{3} + G)}}{b}$

$A = - \frac{\sqrt{b (5 h^{3} + G)}}{b}$

$A = \frac{\sqrt{b (5 h^{3} + G)}}{b}$

$A = - \frac{\sqrt{b (5 h^{3} + G)}}{b}$

Solve for A 5h^3=bA^2-G

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