Solve Using the Quadratic Formula 3x^2+10x-32=0

$3 x^{2} + 10 x - 32 = 0$

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 $a = 3$ , $b = 10$ , and $c = - 32$ into the quadratic formula and solve for $x$ .

$\frac{- 10 \pm \sqrt{10^{2} - 4 \cdot (3 \cdot - 32)}}{2 \cdot 3}$

Step 3

Simplify.

Simplify the numerator.

Raise $10$ to the power of $2$ .

$x = \frac{- 10 \pm \sqrt{100 - 4 \cdot 3 \cdot - 32}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot - 32$ .

Multiply $- 4$ by $3$ .

$x = \frac{- 10 \pm \sqrt{100 - 12 \cdot - 32}}{2 \cdot 3}$

Multiply $- 12$ by $- 32$ .

$x = \frac{- 10 \pm \sqrt{100 + 384}}{2 \cdot 3}$

Add $100$ and $384$ .

$x = \frac{- 10 \pm \sqrt{484}}{2 \cdot 3}$

Rewrite $484$ as $22^{2}$ .

$x = \frac{- 10 \pm \sqrt{22^{2}}}{2 \cdot 3}$

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

$x = \frac{- 10 \pm 22}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{- 10 \pm 22}{6}$

Simplify $\frac{- 10 \pm 22}{6}$ .

$x = \frac{- 5 \pm 11}{3}$

Step 4

The final answer is the combination of both solutions.

$x = 2, - \frac{16}{3}$