Find All Complex Solutions 3x^2-4=0

$3 x^{2} - 4 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 3$ , $b = 0$ , and $c = - 4$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (3 \cdot - 4)}}{2 \cdot 3}$

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 3 \cdot - 4}}{2 \cdot 3}$

Multiply $- 4$ by $3$ .

$x = \frac{0 \pm \sqrt{0 - 12 \cdot - 4}}{2 \cdot 3}$

Multiply $- 12$ by $- 4$ .

$x = \frac{0 \pm \sqrt{0 + 48}}{2 \cdot 3}$

Add $0$ and $48$ .

$x = \frac{0 \pm \sqrt{48}}{2 \cdot 3}$

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$x = \frac{0 \pm \sqrt{16 (3)}}{2 \cdot 3}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{0 \pm \sqrt{4^{2} \cdot 3}}{2 \cdot 3}$

Pull terms out from under the radical.

$x = \frac{0 \pm 4 \sqrt{3}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{0 \pm 4 \sqrt{3}}{6}$

Simplify $\frac{0 \pm 4 \sqrt{3}}{6}$ .

$x = \frac{\pm 2 \sqrt{3}}{3}$

The final answer is the combination of both solutions.

$x = \frac{2 \sqrt{3}}{3}, - \frac{2 \sqrt{3}}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2 \sqrt{3}}{3}, - \frac{2 \sqrt{3}}{3}$

Decimal Form:

$x = 1.15470053 \dots, - 1.15470053 \dots$