Solve Using the Quadratic Formula 2x^2+6x-216=0

$2 x^{2} + 6 x - 216 = 0$

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 $a = 2$ , $b = 6$ , and $c = - 216$ into the quadratic formula and solve for $x$ .

$\frac{- 6 \pm \sqrt{6^{2} - 4 \cdot (2 \cdot - 216)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

Raise $6$ to the power of $2$ .

$x = \frac{- 6 \pm \sqrt{36 - 4 \cdot 2 \cdot - 216}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 216$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 6 \pm \sqrt{36 - 8 \cdot - 216}}{2 \cdot 2}$

Multiply $- 8$ by $- 216$ .

$x = \frac{- 6 \pm \sqrt{36 + 1728}}{2 \cdot 2}$

Add $36$ and $1728$ .

$x = \frac{- 6 \pm \sqrt{1764}}{2 \cdot 2}$

Rewrite $1764$ as $42^{2}$ .

$x = \frac{- 6 \pm \sqrt{42^{2}}}{2 \cdot 2}$

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

$x = \frac{- 6 \pm 42}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 6 \pm 42}{4}$

Simplify $\frac{- 6 \pm 42}{4}$ .

$x = \frac{- 3 \pm 21}{2}$

Step 4

The final answer is the combination of both solutions.

$x = 9, - 12$