Solve -q(p)=-p^2+57

$$- q ( p ) = - p ^ { 2 } + 57$$

Solve for q

$$q=p-\frac{57}{p}$$

$$p\neq 0$$

Steps for Solving Linear Equation

Reorder the terms.

$$-pq=-p^{2}+57$$

The equation is in standard form.

$$\left(-p\right)q=57-p^{2}$$

Divide both sides by -p.

$$\frac{\left(-p\right)q}{-p}=\frac{57-p^{2}}{-p}$$

Dividing by -p undoes the multiplication by -p.

$$q=\frac{57-p^{2}}{-p}$$

Divide -p^{2}+57 by -p.

$$q=p-\frac{57}{p}$$

Solve for p

$$p=\frac{\sqrt{q^{2}+228}+q}{2}$$

$$p=\frac{-\sqrt{q^{2}+228}+q}{2}$$