Solve Using the Quadratic Formula 3x^2-9=0

$3 x^{2} - 9 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 3$ , $b = 0$ , and $c = - 9$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (3 \cdot - 9)}}{2 \cdot 3}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 3 \cdot - 9}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot - 9$ .

Multiply $- 4$ by $3$ .

$x = \frac{0 \pm \sqrt{0 - 12 \cdot - 9}}{2 \cdot 3}$

Multiply $- 12$ by $- 9$ .

$x = \frac{0 \pm \sqrt{0 + 108}}{2 \cdot 3}$

Add $0$ and $108$ .

$x = \frac{0 \pm \sqrt{108}}{2 \cdot 3}$

Rewrite $108$ as $6^{2} \cdot 3$ .

Factor $36$ out of $108$ .

$x = \frac{0 \pm \sqrt{36 (3)}}{2 \cdot 3}$

Rewrite $36$ as $6^{2}$ .

$x = \frac{0 \pm \sqrt{6^{2} \cdot 3}}{2 \cdot 3}$

Pull terms out from under the radical.

$x = \frac{0 \pm 6 \sqrt{3}}{2 \cdot 3}$

Multiply $2$ by $3$ .

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

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

$x = \pm \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{3}$

Decimal Form:

$x = 1.73205080 \dots, - 1.73205080 \dots$