Solve Using the Quadratic Formula 2x^2-7x+9=0

$2 x^{2} - 7 x + 9 = 0$

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 $a = 2$ , $b = - 7$ , and $c = 9$ into the quadratic formula and solve for $x$ .

$\frac{7 \pm \sqrt{{(- 7)}^{2} - 4 \cdot (2 \cdot 9)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 7$ to the power of $2$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot 2 \cdot 9}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot 9$ .

Multiply $- 4$ by $2$ .

$x = \frac{7 \pm \sqrt{49 - 8 \cdot 9}}{2 \cdot 2}$

Multiply $- 8$ by $9$ .

$x = \frac{7 \pm \sqrt{49 - 72}}{2 \cdot 2}$

Subtract $72$ from $49$ .

$x = \frac{7 \pm \sqrt{- 23}}{2 \cdot 2}$

Rewrite $- 23$ as $- 1 (23)$ .

$x = \frac{7 \pm \sqrt{- 1 \cdot 23}}{2 \cdot 2}$

Rewrite $\sqrt{- 1 (23)}$ as $\sqrt{- 1} \cdot \sqrt{23}$ .

$x = \frac{7 \pm \sqrt{- 1} \cdot \sqrt{23}}{2 \cdot 2}$

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

$x = \frac{7 \pm i \sqrt{23}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{7 \pm i \sqrt{23}}{4}$