Solve 9x^2+3kx+4=0

$$9 x ^ { 2 } + 3 k x + 4 = 0$$

Solve for k

$$k=-3x-\frac{4}{3x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 9x^{2} from both sides. Anything subtracted from zero gives its negation.

$$3kx+4=-9x^{2}$$

Subtract 4 from both sides.

$$3kx=-9x^{2}-4$$

The equation is in standard form.

$$3xk=-9x^{2}-4$$

Divide both sides by 3x.

$$\frac{3xk}{3x}=\frac{-9x^{2}-4}{3x}$$

Dividing by 3x undoes the multiplication by 3x.

$$k=\frac{-9x^{2}-4}{3x}$$

Divide -9x^{2}-4 by 3x.

$$k=-3x-\frac{4}{3x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{k^{2}-16}-k}{6}$$

$$x=\frac{-\sqrt{k^{2}-16}-k}{6}$$

Solve for x

$$x=\frac{\sqrt{k^{2}-16}-k}{6}$$

$$x=\frac{-\sqrt{k^{2}-16}-k}{6}\text{, }|k|\geq 4$$