Solve (A):P(A)=1:2f

$$( A ) : P ( A ) = 1 : 2 f$$

Solve for P

$$\left\{\begin{matrix}P=\frac{2A^{2}}{f}\text{, }&A\neq 0\text{ and }f\neq 0\\P\neq 0\text{, }&f=0\text{ and }A=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable P cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2P, the least common multiple of P,2.

$$2AA=\frac{1}{2}f\times 2P$$

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

$$2A^{2}=\frac{1}{2}f\times 2P$$

Multiply \frac{1}{2} and 2 to get 1.

$$2A^{2}=fP$$

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

$$fP=2A^{2}$$

Divide both sides by f.

$$\frac{fP}{f}=\frac{2A^{2}}{f}$$

Dividing by f undoes the multiplication by f.

$$P=\frac{2A^{2}}{f}$$

Variable P cannot be equal to 0.

$$P=\frac{2A^{2}}{f}\text{, }P\neq 0$$

Solve for A (complex solution)

$$A=-\frac{\sqrt{P}\sqrt{2f}}{2}$$

$$A=\frac{\sqrt{P}\sqrt{2f}}{2}\text{, }P\neq 0$$

Solve for A

$$A=\frac{\sqrt{2Pf}}{2}$$

$$A=-\frac{\sqrt{2Pf}}{2}\text{, }\left(f\geq 0\text{ and }P>0\right)\text{ or }\left(f\leq 0\text{ and }P<0\right)$$