Solve for L h=(L^2)/(f*c)

$h = \frac{L^{2}}{f \cdot c}$

Rewrite the equation as $\frac{L^{2}}{f \cdot c} = h$ .

$\frac{L^{2}}{f \cdot c} = h$

Multiply both sides by $f \cdot c$ .

$\frac{L^{2}}{f \cdot c} (f \cdot c) = h (f \cdot c)$

Simplify.

Simplify the left side.

Cancel the common factor of $f \cdot c$ .

Cancel the common factor.

$\frac{L^{2}}{f \cdot c} (f \cdot c) = h (f \cdot c)$

Rewrite the expression.

$L^{2} = h (f \cdot c)$

Simplify the right side.

Remove parentheses.

$L^{2} = h f c$

Solve for $L$ .

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

$L = \pm \sqrt{h f c}$

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.

$L = \sqrt{h f c}$

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

$L = - \sqrt{h f c}$

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

$L = \sqrt{h f c}$

$L = - \sqrt{h f c}$

$L = \sqrt{h f c}$

$L = - \sqrt{h f c}$

$L = \sqrt{h f c}$

$L = - \sqrt{h f c}$