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

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

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 $a = 3$ , $b = - 2$ , and $c = - 2$ into the quadratic formula and solve for $x$ .

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

Step 3

Simplify.

Simplify the numerator.

Raise $- 2$ to the power of $2$ .

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

Multiply $- 4 \cdot 3 \cdot - 2$ .

Multiply $- 4$ by $3$ .

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

Multiply $- 12$ by $- 2$ .

$x = \frac{2 \pm \sqrt{4 + 24}}{2 \cdot 3}$

Add $4$ and $24$ .

$x = \frac{2 \pm \sqrt{28}}{2 \cdot 3}$

Rewrite $28$ as $2^{2} \cdot 7$ .

Factor $4$ out of $28$ .

$x = \frac{2 \pm \sqrt{4 (7)}}{2 \cdot 3}$

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

$x = \frac{2 \pm \sqrt{2^{2} \cdot 7}}{2 \cdot 3}$

Pull terms out from under the radical.

$x = \frac{2 \pm 2 \sqrt{7}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{2 \pm 2 \sqrt{7}}{6}$

Simplify $\frac{2 \pm 2 \sqrt{7}}{6}$ .

$x = \frac{1 \pm \sqrt{7}}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1 \pm \sqrt{7}}{3}$

Decimal Form:

$x = 1.21525043 \dots, - 0.54858377 \dots$