Solve Using the Quadratic Formula 3x^2+3x-6=0

$3 x^{2} + 3 x - 6 = 0$

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 $a = 3$ , $b = 3$ , and $c = - 6$ into the quadratic formula and solve for $x$ .

$\frac{- 3 \pm \sqrt{3^{2} - 4 \cdot (3 \cdot - 6)}}{2 \cdot 3}$

Step 3

Simplify.

Simplify the numerator.

Raise $3$ to the power of $2$ .

$x = \frac{- 3 \pm \sqrt{9 - 4 \cdot 3 \cdot - 6}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot - 6$ .

Multiply $- 4$ by $3$ .

$x = \frac{- 3 \pm \sqrt{9 - 12 \cdot - 6}}{2 \cdot 3}$

Multiply $- 12$ by $- 6$ .

$x = \frac{- 3 \pm \sqrt{9 + 72}}{2 \cdot 3}$

Add $9$ and $72$ .

$x = \frac{- 3 \pm \sqrt{81}}{2 \cdot 3}$

Rewrite $81$ as $9^{2}$ .

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

Pull terms out from under the radical, assuming positive real numbers.

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

Multiply $2$ by $3$ .

$x = \frac{- 3 \pm 9}{6}$

Simplify $\frac{- 3 \pm 9}{6}$ .

$x = \frac{- 1 \pm 3}{2}$

Step 4

The final answer is the combination of both solutions.

$x = 1, - 2$