Solve S=5uv-v^2

$$S = 5 u v - v ^ { 2 }$$

Solve for u

$$\left\{\begin{matrix}u=\frac{v^{2}+S}{5v}\text{, }&v\neq 0\\u\in \mathrm{R}\text{, }&S=0\text{ and }v=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$5uv-v^{2}=S$$

Add v^{2} to both sides.

$$5uv=S+v^{2}$$

The equation is in standard form.

$$5vu=v^{2}+S$$

Divide both sides by 5v.

$$\frac{5vu}{5v}=\frac{v^{2}+S}{5v}$$

Dividing by 5v undoes the multiplication by 5v.

$$u=\frac{v^{2}+S}{5v}$$

Solve for S

$$S=-v\left(v-5u\right)$$