Solve 3x^2+4sqrt{3}=2

$$3 { x }^{ 2 } +4 \sqrt{ 3 } =2$$

Solve for x (complex solution)

$$x=-\frac{i\sqrt{12\sqrt{3}-6}}{3}\approx -0-1.281692011i$$

$$x=\frac{i\sqrt{12\sqrt{3}-6}}{3}\approx 1.281692011i$$

Steps by Finding Square Root

Subtract 4\sqrt{3} from both sides.

$$3x^{2}=2-4\sqrt{3}$$

Dividing by 3 undoes the multiplication by 3.

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

Take the square root of both sides of the equation.

$$x=\frac{i\sqrt{12\sqrt{3}-6}}{3} x=-\frac{i\sqrt{12\sqrt{3}-6}}{3}$$

Steps Using the Quadratic Formula

Subtract 2 from both sides.

$$3x^{2}+4\sqrt{3}-2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 4\sqrt{3}-2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(4\sqrt{3}-2\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(4\sqrt{3}-2\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(4\sqrt{3}-2\right)}}{2\times 3}$$

Multiply -12 times 4\sqrt{3}-2.

$$x=\frac{0±\sqrt{24-48\sqrt{3}}}{2\times 3}$$

Take the square root of -48\sqrt{3}+24.

$$x=\frac{0±2i\sqrt{12\sqrt{3}-6}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±2i\sqrt{12\sqrt{3}-6}}{6}$$

Now solve the equation x=\frac{0±2i\sqrt{12\sqrt{3}-6}}{6} when ± is plus.

$$x=\frac{i\sqrt{12\sqrt{3}-6}}{3}$$

Now solve the equation x=\frac{0±2i\sqrt{12\sqrt{3}-6}}{6} when ± is minus.

$$x=-\frac{i\sqrt{12\sqrt{3}-6}}{3}$$

The equation is now solved.

$$x=\frac{i\sqrt{12\sqrt{3}-6}}{3} x=-\frac{i\sqrt{12\sqrt{3}-6}}{3}$$