Solve 3x^2+2ax+3=0

$$3 x ^ { 2 } + 2 a x + 3 = 0$$

Solve for a

$$a=-\frac{3x}{2}-\frac{3}{2x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 3x^{2} from both sides. Anything subtracted from zero gives its negation.

$$2ax+3=-3x^{2}$$

Subtract 3 from both sides.

$$2ax=-3x^{2}-3$$

The equation is in standard form.

$$2xa=-3x^{2}-3$$

Divide both sides by 2x.

$$\frac{2xa}{2x}=\frac{-3x^{2}-3}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$a=\frac{-3x^{2}-3}{2x}$$

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

$$a=-\frac{3x}{2}-\frac{3}{2x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{a^{2}-9}-a}{3}$$

$$x=\frac{-\sqrt{a^{2}-9}-a}{3}$$

Solve for x

$$x=\frac{\sqrt{a^{2}-9}-a}{3}$$

$$x=\frac{-\sqrt{a^{2}-9}-a}{3}\text{, }|a|\geq 3$$