Solve y=25x^2+20x+a

$$y = 25 x ^ { 2 } + 20 x + a$$

Solve for a

$$a=y-20x-25x^{2}$$

Solution Steps

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

$$25x^{2}+20x+a=y$$

Subtract 25x^{2} from both sides.

$$20x+a=y-25x^{2}$$

Subtract 20x from both sides.

$$a=y-25x^{2}-20x$$

Solve for x (complex solution)

$$x=\frac{\sqrt{y-a+4}-2}{5}$$

$$x=\frac{-\sqrt{y-a+4}-2}{5}$$

Solve for x

$$x=\frac{\sqrt{y-a+4}-2}{5}$$

$$x=\frac{-\sqrt{y-a+4}-2}{5}\text{, }y\geq a-4$$