Solve ap=b/a

$$a p = \frac { b } { a }$$

Solve for b

$$b=pa^{2}$$

$$a\neq 0$$

Solution Steps

Multiply both sides of the equation by a.

$$apa=b$$

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

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

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

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

Solve for a (complex solution)

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

Solve for a

$$\left\{\begin{matrix}a=\sqrt{\frac{b}{p}}\text{; }a=-\sqrt{\frac{b}{p}}\text{, }&\left(p<0\text{ and }b<0\right)\text{ or }\left(p>0\text{ and }b>0\right)\\a\neq 0\text{, }&b=0\text{ and }p=0\end{matrix}\right.$$