Solve Using the Quadratic Formula 9x^2+12x=32

$9 x^{2} + 12 x = 32$

Step 1

Subtract $32$ from both sides of the equation.

$9 x^{2} + 12 x - 32 = 0$

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 $a = 9$ , $b = 12$ , and $c = - 32$ into the quadratic formula and solve for $x$ .

$\frac{- 12 \pm \sqrt{12^{2} - 4 \cdot (9 \cdot - 32)}}{2 \cdot 9}$

Step 4

Simplify.

Simplify the numerator.

Raise $12$ to the power of $2$ .

$x = \frac{- 12 \pm \sqrt{144 - 4 \cdot 9 \cdot - 32}}{2 \cdot 9}$

Multiply $- 4 \cdot 9 \cdot - 32$ .

Multiply $- 4$ by $9$ .

$x = \frac{- 12 \pm \sqrt{144 - 36 \cdot - 32}}{2 \cdot 9}$

Multiply $- 36$ by $- 32$ .

$x = \frac{- 12 \pm \sqrt{144 + 1152}}{2 \cdot 9}$

Add $144$ and $1152$ .

$x = \frac{- 12 \pm \sqrt{1296}}{2 \cdot 9}$

Rewrite $1296$ as $36^{2}$ .

$x = \frac{- 12 \pm \sqrt{36^{2}}}{2 \cdot 9}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{- 12 \pm 36}{2 \cdot 9}$

Multiply $2$ by $9$ .

$x = \frac{- 12 \pm 36}{18}$

Simplify $\frac{- 12 \pm 36}{18}$ .

$x = \frac{- 2 \pm 6}{3}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{4}{3}, - \frac{8}{3}$