Solve S=h^2/r_{0}/w^2*r_{1}

$$S = \frac { h ^ { 2 } } { r _ { 0 } } / w ^ { 2 } \cdot r _ { 1 }$$

Solve for h (complex solution)

$$\left\{\begin{matrix}h=-r_{1}^{-\frac{1}{2}}\sqrt{S}\sqrt{r_{0}}w\text{; }h=r_{1}^{-\frac{1}{2}}\sqrt{S}\sqrt{r_{0}}w\text{, }&r_{0}\neq 0\text{ and }r_{1}\neq 0\text{ and }w\neq 0\\h\in \mathrm{C}\text{, }&S=0\text{ and }r_{1}=0\text{ and }w\neq 0\text{ and }r_{0}\neq 0\end{matrix}\right.$$

Solve for S

$$S=\frac{\left(\frac{h}{w}\right)^{2}r_{1}}{r_{0}}$$

$$r_{0}\neq 0\text{ and }w\neq 0$$

Solve for h

$$\left\{\begin{matrix}h=w\sqrt{\frac{Sr_{0}}{r_{1}}}\text{; }h=-w\sqrt{\frac{Sr_{0}}{r_{1}}}\text{, }&\left(r_{1}>0\text{ or }r_{0}<0\text{ or }S\leq 0\right)\text{ and }r_{1}\neq 0\text{ and }\left(r_{0}<0\text{ or }S\geq 0\text{ or }r_{1}<0\right)\text{ and }w\neq 0\text{ and }\left(r_{1}>0\text{ or }S\geq 0\text{ or }r_{0}>0\right)\text{ and }r_{0}\neq 0\text{ and }\left(r_{0}>0\text{ or }r_{1}<0\text{ or }S\leq 0\right)\\h\in \mathrm{R}\text{, }&S=0\text{ and }r_{1}=0\text{ and }w\neq 0\text{ and }r_{0}\neq 0\end{matrix}\right.$$