Solve S=abquad(a)

$$S = a b \quad ( a )$$

Solve for S

$$S=ba^{2}$$

Solution Steps

Multiply a and a to get a^{2}.

$$S=a^{2}b$$

Solve for a (complex solution)

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

Solve for a

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