Solve Using the Quadratic Formula 15x^2-2x-8=0

$15 x^{2} - 2 x - 8 = 0$

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 $a = 15$ , $b = - 2$ , and $c = - 8$ into the quadratic formula and solve for $x$ .

$\frac{2 \pm \sqrt{{(- 2)}^{2} - 4 \cdot (15 \cdot - 8)}}{2 \cdot 15}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{2 \pm \sqrt{4 - 4 \cdot 15 \cdot - 8}}{2 \cdot 15}$

Multiply $- 4 \cdot 15 \cdot - 8$ .

Multiply $- 4$ by $15$ .

$x = \frac{2 \pm \sqrt{4 - 60 \cdot - 8}}{2 \cdot 15}$

Multiply $- 60$ by $- 8$ .

$x = \frac{2 \pm \sqrt{4 + 480}}{2 \cdot 15}$

Add $4$ and $480$ .

$x = \frac{2 \pm \sqrt{484}}{2 \cdot 15}$

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

$x = \frac{2 \pm \sqrt{22^{2}}}{2 \cdot 15}$

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

$x = \frac{2 \pm 22}{2 \cdot 15}$

Multiply $2$ by $15$ .

$x = \frac{2 \pm 22}{30}$

Simplify $\frac{2 \pm 22}{30}$ .

$x = \frac{1 \pm 11}{15}$

Step 4

The final answer is the combination of both solutions.

$x = \frac{4}{5}, - \frac{2}{3}$