Solve Q=(1.00/n)A(R_h^2/3)S^1/2

$$Q = ( 1.00 / n ) A ( R _ { h } ^ { 2 / 3 } ) S ^ { 1 / 2 }$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=R_{h}^{-\frac{2}{3}}S^{-\frac{1}{2}}Qn\text{, }&n\neq 0\text{ and }S\neq 0\text{ and }R_{h}\neq 0\\A\in \mathrm{C}\text{, }&\left(S=0\text{ or }R_{h}=0\right)\text{ and }Q=0\text{ and }n\neq 0\end{matrix}\right.$$

Solve for Q (complex solution)

$$Q=\frac{\sqrt{S}R_{h}^{\frac{2}{3}}A}{n}$$

$$n\neq 0$$

Solve for A

$$\left\{\begin{matrix}A=\frac{Qn}{\sqrt{S}R_{h}^{\frac{2}{3}}}\text{, }&n\neq 0\text{ and }R_{h}\neq 0\text{ and }S>0\\A\in \mathrm{R}\text{, }&S\geq 0\text{ and }\left(S=0\text{ or }R_{h}=0\right)\text{ and }n\neq 0\text{ and }Q=0\end{matrix}\right.$$

Solve for Q

$$Q=\frac{\sqrt{S}R_{h}^{\frac{2}{3}}A}{n}$$

$$n\neq 0\text{ and }S\geq 0$$