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

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

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 $a = 2$ , $b = 3$ , and $c = 6$ into the quadratic formula and solve for $x$ .

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

Step 3

Simplify.

Simplify the numerator.

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

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

Multiply $- 4 \cdot 2 \cdot 6$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 3 \pm \sqrt{9 - 8 \cdot 6}}{2 \cdot 2}$

Multiply $- 8$ by $6$ .

$x = \frac{- 3 \pm \sqrt{9 - 48}}{2 \cdot 2}$

Subtract $48$ from $9$ .

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

Rewrite $- 39$ as $- 1 (39)$ .

$x = \frac{- 3 \pm \sqrt{- 1 \cdot 39}}{2 \cdot 2}$

Rewrite $\sqrt{- 1 (39)}$ as $\sqrt{- 1} \cdot \sqrt{39}$ .

$x = \frac{- 3 \pm \sqrt{- 1} \cdot \sqrt{39}}{2 \cdot 2}$

Rewrite $\sqrt{- 1}$ as $i$ .

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

Multiply $2$ by $2$ .

$x = \frac{- 3 \pm i \sqrt{39}}{4}$