Question

$$\pi n^{2}=\frac{22}{X}\times\frac{y}{2}\times\frac{7}{2}\times\frac{77}{2}$$

Solve for X

$\left\{\begin{matrix}X=\frac{5929y}{4\pi n^{2}}\text{, }&y\neq 0\text{ and }n\neq 0\\X\neq 0\text{, }&n=0\text{ and }y=0\end{matrix}\right.$

Show Solution

Solve for n (complex solution)

$n=-\frac{77\left(\pi X\right)^{-\frac{1}{2}}\sqrt{y}}{2}$
$n=\frac{77\left(\pi X\right)^{-\frac{1}{2}}\sqrt{y}}{2}\text{, }X\neq 0$

Solve for n

$n=\frac{77\sqrt{\frac{y}{\pi X}}}{2}$
$n=-\frac{77\sqrt{\frac{y}{\pi X}}}{2}\text{, }\left(y\geq 0\text{ and }X>0\right)\text{ or }\left(y\leq 0\text{ and }X<0\right)$