Solve Using the Quadratic Formula -4x^2=5x+9

$- 4 x^{2} = 5 x + 9$

Step 1

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

Subtract $5 x$ from both sides of the equation.

$- 4 x^{2} - 5 x = 9$

Subtract $9$ from both sides of the equation.

$- 4 x^{2} - 5 x - 9 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = - 4$ , $b = - 5$ , and $c = - 9$ into the quadratic formula and solve for $x$ .

$\frac{5 \pm \sqrt{{(- 5)}^{2} - 4 \cdot (- 4 \cdot - 9)}}{2 \cdot - 4}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 5$ to the power of $2$ .

$x = \frac{5 \pm \sqrt{25 - 4 \cdot - 4 \cdot - 9}}{2 \cdot - 4}$

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

Multiply $- 4$ by $- 4$ .

$x = \frac{5 \pm \sqrt{25 + 16 \cdot - 9}}{2 \cdot - 4}$

Multiply $16$ by $- 9$ .

$x = \frac{5 \pm \sqrt{25 - 144}}{2 \cdot - 4}$

Subtract $144$ from $25$ .

$x = \frac{5 \pm \sqrt{- 119}}{2 \cdot - 4}$

Rewrite $- 119$ as $- 1 (119)$ .

$x = \frac{5 \pm \sqrt{- 1 \cdot 119}}{2 \cdot - 4}$

Rewrite $\sqrt{- 1 (119)}$ as $\sqrt{- 1} \cdot \sqrt{119}$ .

$x = \frac{5 \pm \sqrt{- 1} \cdot \sqrt{119}}{2 \cdot - 4}$

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

$x = \frac{5 \pm i \sqrt{119}}{2 \cdot - 4}$

Multiply $2$ by $- 4$ .

$x = \frac{5 \pm i \sqrt{119}}{- 8}$

Move the negative in front of the fraction.

$x = - \frac{5 \pm i \sqrt{119}}{8}$