Solve 0.25z_{0}=ku^2

$$0.25 z _ { 0 } = k u ^ { 2 }$$

Solve for k

$$\left\{\begin{matrix}k=\frac{z_{0}}{4u^{2}}\text{, }&u\neq 0\\k\in \mathrm{R}\text{, }&z_{0}=0\text{ and }u=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ku^{2}=0.25z_{0}$$

The equation is in standard form.

$$u^{2}k=\frac{z_{0}}{4}$$

Divide both sides by u^{2}.

$$\frac{u^{2}k}{u^{2}}=\frac{z_{0}}{4u^{2}}$$

Dividing by u^{2} undoes the multiplication by u^{2}.

$$k=\frac{z_{0}}{4u^{2}}$$

Solve for u

$$\left\{\begin{matrix}u=\frac{\sqrt{\frac{z_{0}}{k}}}{2}\text{; }u=-\frac{\sqrt{\frac{z_{0}}{k}}}{2}\text{, }&\left(z_{0}\geq 0\text{ and }k>0\right)\text{ or }\left(z_{0}\leq 0\text{ and }k<0\right)\\u\in \mathrm{R}\text{, }&z_{0}=0\text{ and }k=0\end{matrix}\right.$$