Solve 5x^2+px+4=0

$$5 x ^ { 2 } + p x + 4 = 0$$

Solve for p

$$p=-5x-\frac{4}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$px+4=-5x^{2}$$

Subtract 4 from both sides.

$$px=-5x^{2}-4$$

The equation is in standard form.

$$xp=-5x^{2}-4$$

Divide both sides by x.

$$\frac{xp}{x}=\frac{-5x^{2}-4}{x}$$

Dividing by x undoes the multiplication by x.

$$p=\frac{-5x^{2}-4}{x}$$

Divide -5x^{2}-4 by x.

$$p=-5x-\frac{4}{x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{p^{2}-80}-p}{10}$$

$$x=\frac{-\sqrt{p^{2}-80}-p}{10}$$

Solve for x

$$x=\frac{\sqrt{p^{2}-80}-p}{10}$$

$$x=\frac{-\sqrt{p^{2}-80}-p}{10}\text{, }|p|\geq 4\sqrt{5}$$