Solve Using the Quadratic Formula 3x^2+9x+17=0

$3 x^{2} + 9 x + 17 = 0$

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 $a = 3$ , $b = 9$ , and $c = 17$ into the quadratic formula and solve for $x$ .

$\frac{- 9 \pm \sqrt{9^{2} - 4 \cdot (3 \cdot 17)}}{2 \cdot 3}$

Step 3

Simplify.

Simplify the numerator.

Raise $9$ to the power of $2$ .

$x = \frac{- 9 \pm \sqrt{81 - 4 \cdot 3 \cdot 17}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot 17$ .

Multiply $- 4$ by $3$ .

$x = \frac{- 9 \pm \sqrt{81 - 12 \cdot 17}}{2 \cdot 3}$

Multiply $- 12$ by $17$ .

$x = \frac{- 9 \pm \sqrt{81 - 204}}{2 \cdot 3}$

Subtract $204$ from $81$ .

$x = \frac{- 9 \pm \sqrt{- 123}}{2 \cdot 3}$

Rewrite $- 123$ as $- 1 (123)$ .

$x = \frac{- 9 \pm \sqrt{- 1 \cdot 123}}{2 \cdot 3}$

Rewrite $\sqrt{- 1 (123)}$ as $\sqrt{- 1} \cdot \sqrt{123}$ .

$x = \frac{- 9 \pm \sqrt{- 1} \cdot \sqrt{123}}{2 \cdot 3}$

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

$x = \frac{- 9 \pm i \sqrt{123}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{- 9 \pm i \sqrt{123}}{6}$