Solve Using the Quadratic Formula 3x^2-39=0

$3 x^{2} - 39 = 0$

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 $c = - 39$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (3 \cdot - 39)}}{2 \cdot 3}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 3 \cdot - 39}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot - 39$ .

Multiply $- 4$ by $3$ .

$x = \frac{0 \pm \sqrt{0 - 12 \cdot - 39}}{2 \cdot 3}$

Multiply $- 12$ by $- 39$ .

$x = \frac{0 \pm \sqrt{0 + 468}}{2 \cdot 3}$

Add $0$ and $468$ .

$x = \frac{0 \pm \sqrt{468}}{2 \cdot 3}$

Rewrite $468$ as $6^{2} \cdot 13$ .

Factor $36$ out of $468$ .

$x = \frac{0 \pm \sqrt{36 (13)}}{2 \cdot 3}$

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

$x = \frac{0 \pm \sqrt{6^{2} \cdot 13}}{2 \cdot 3}$

Pull terms out from under the radical.

$x = \frac{0 \pm 6 \sqrt{13}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{0 \pm 6 \sqrt{13}}{6}$

Simplify $\frac{0 \pm 6 \sqrt{13}}{6}$ .

$x = \pm \sqrt{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{13}$

Decimal Form:

$x = 3.60555127 \dots, - 3.60555127 \dots$