Solve x^2+(5k+2)x+20=0

$$x ^ { 2 } + ( 5 k + 2 ) x + 20 = 0$$

Solve for k

$$k=-\frac{x}{5}-\frac{2}{5}-\frac{4}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5k+2 by x.

$$x^{2}+5kx+2x+20=0$$

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

$$5kx+2x+20=-x^{2}$$

Subtract 2x from both sides.

$$5kx+20=-x^{2}-2x$$

Subtract 20 from both sides.

$$5kx=-x^{2}-2x-20$$

The equation is in standard form.

$$5xk=-x^{2}-2x-20$$

Divide both sides by 5x.

$$\frac{5xk}{5x}=\frac{-x^{2}-2x-20}{5x}$$

Dividing by 5x undoes the multiplication by 5x.

$$k=\frac{-x^{2}-2x-20}{5x}$$

Divide -x^{2}-2x-20 by 5x.

$$k=-\frac{x}{5}-\frac{2}{5}-\frac{4}{x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{25k^{2}+20k-76}}{2}-\frac{5k}{2}-1$$

$$x=-\frac{\sqrt{25k^{2}+20k-76}}{2}-\frac{5k}{2}-1$$

Solve for x

$$x=\frac{\sqrt{25k^{2}+20k-76}}{2}-\frac{5k}{2}-1$$

$$x=-\frac{\sqrt{25k^{2}+20k-76}}{2}-\frac{5k}{2}-1\text{, }k\geq \frac{4\sqrt{5}-2}{5}\text{ or }k\leq \frac{-4\sqrt{5}-2}{5}$$