Solve for a q = square root of fa-H

$q = \sqrt{f a - H}$

Rewrite the equation as $\sqrt{f a - H} = q$ .

$\sqrt{f a - H} = q$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{f a - H}}^{2} = q^{2}$

Simplify each side of the equation.

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

${({(f a - H)}^{\frac{1}{2}})}^{2} = q^{2}$

Simplify the left side.

Simplify ${({(f a - H)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(f a - H)}^{\frac{1}{2}})}^{2}$ .

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

${(f a - H)}^{\frac{1}{2} \cdot 2} = q^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(f a - H)}^{\frac{1}{2} \cdot 2} = q^{2}$

Rewrite the expression.

${(f a - H)}^{1} = q^{2}$

Simplify.

$f a - H = q^{2}$

Solve for $a$ .

Add $H$ to both sides of the equation.

$f a = q^{2} + H$

Divide each term in $f a = q^{2} + H$ by $f$ and simplify.

Divide each term in $f a = q^{2} + H$ by $f$ .

$\frac{f a}{f} = \frac{q^{2}}{f} + \frac{H}{f}$

Simplify the left side.

Cancel the common factor of $f$ .

Cancel the common factor.

$\frac{f a}{f} = \frac{q^{2}}{f} + \frac{H}{f}$

Divide $a$ by $1$ .

$a = \frac{q^{2}}{f} + \frac{H}{f}$