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

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

Move all the expressions to the left side of the equation.

Subtract $2 x^{2}$ from both sides of the equation.

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

Subtract $9$ from both sides of the equation.

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

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

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

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

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 $- 4$ 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 $- 2$ .

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

Move the negative in front of the fraction.

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