Solve px^2-q=r

$$p x ^ { 2 } - q = r$$

Solve for p

$$\left\{\begin{matrix}p=\frac{q+r}{x^{2}}\text{, }&x\neq 0\\p\in \mathrm{R}\text{, }&q=-r\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add q to both sides.

$$px^{2}=r+q$$

The equation is in standard form.

$$x^{2}p=q+r$$

Divide both sides by x^{2}.

$$\frac{x^{2}p}{x^{2}}=\frac{q+r}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$p=\frac{q+r}{x^{2}}$$

Solve for q

$$q=px^{2}-r$$

Steps for Solving Linear Equation

Subtract px^{2} from both sides.

$$-q=r-px^{2}$$

Divide both sides by -1.

$$\frac{-q}{-1}=\frac{r-px^{2}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$q=\frac{r-px^{2}}{-1}$$

Divide -px^{2}+r by -1.

$$q=px^{2}-r$$