Solve L=1/2c_{L}Sv^2

$$L = \frac { 1 } { 2 } c _ { L } S v ^ { 2 }$$

Solve for S

$$\left\{\begin{matrix}S=\frac{2L}{c_{L}v^{2}}\text{, }&v\neq 0\text{ and }c_{L}\neq 0\\S\in \mathrm{R}\text{, }&\left(c_{L}=0\text{ or }v=0\right)\text{ and }L=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{2}c_{L}Sv^{2}=L$$

The equation is in standard form.

$$\frac{c_{L}v^{2}}{2}S=L$$

Divide both sides by \frac{1}{2}c_{L}v^{2}.

$$\frac{2\times \frac{c_{L}v^{2}}{2}S}{c_{L}v^{2}}=\frac{2L}{c_{L}v^{2}}$$

Dividing by \frac{1}{2}c_{L}v^{2} undoes the multiplication by \frac{1}{2}c_{L}v^{2}.

$$S=\frac{2L}{c_{L}v^{2}}$$

Solve for L

$$L=\frac{Sc_{L}v^{2}}{2}$$