Solve 5x^2+9x+h=0

$$5 x ^ { 2 } + 9 x + h = 0$$

Solve for h

$$h=-x\left(5x+9\right)$$

Solution Steps

Subtract 5x^{2} from both sides. Anything subtracted from zero gives its negation.

$$9x+h=-5x^{2}$$

Subtract 9x from both sides.

$$h=-5x^{2}-9x$$

Solve for x (complex solution)

$$x=\frac{\sqrt{81-20h}-9}{10}$$

$$x=\frac{-\sqrt{81-20h}-9}{10}$$

Solve for x

$$x=\frac{\sqrt{81-20h}-9}{10}$$

$$x=\frac{-\sqrt{81-20h}-9}{10}\text{, }h\leq \frac{81}{20}$$