Solve Using the Quadratic Formula 2x^2-9x+12=0

$2 x^{2} - 9 x + 12 = 0$

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 $a = 2$ , $b = - 9$ , and $c = 12$ into the quadratic formula and solve for $x$ .

$\frac{9 \pm \sqrt{{(- 9)}^{2} - 4 \cdot (2 \cdot 12)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{9 \pm \sqrt{81 - 4 \cdot 2 \cdot 12}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot 12$ .

Multiply $- 4$ by $2$ .

$x = \frac{9 \pm \sqrt{81 - 8 \cdot 12}}{2 \cdot 2}$

Multiply $- 8$ by $12$ .

$x = \frac{9 \pm \sqrt{81 - 96}}{2 \cdot 2}$

Subtract $96$ from $81$ .

$x = \frac{9 \pm \sqrt{- 15}}{2 \cdot 2}$

Rewrite $- 15$ as $- 1 (15)$ .

$x = \frac{9 \pm \sqrt{- 1 \cdot 15}}{2 \cdot 2}$

Rewrite $\sqrt{- 1 (15)}$ as $\sqrt{- 1} \cdot \sqrt{15}$ .

$x = \frac{9 \pm \sqrt{- 1} \cdot \sqrt{15}}{2 \cdot 2}$

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

$x = \frac{9 \pm i \sqrt{15}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{9 \pm i \sqrt{15}}{4}$