Solve 4r^2-12r+q=0

$$4 r ^ { 2 } - 12 r + q = 0$$

Solve for q

$$q=-4r\left(r-3\right)$$

Solution Steps

Subtract 4r^{2} from both sides. Anything subtracted from zero gives its negation.

$$-12r+q=-4r^{2}$$

Add 12r to both sides.

$$q=-4r^{2}+12r$$

Solve for r (complex solution)

$$r=\frac{\sqrt{9-q}+3}{2}$$

$$r=\frac{-\sqrt{9-q}+3}{2}$$

Solve for r

$$r=\frac{\sqrt{9-q}+3}{2}$$

$$r=\frac{-\sqrt{9-q}+3}{2}\text{, }q\leq 9$$