Solve Using the Quadratic Formula 8x^2+22x+15=0

$8 x^{2} + 22 x + 15 = 0$

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 $a = 8$ , $b = 22$ , and $c = 15$ into the quadratic formula and solve for $x$ .

$\frac{- 22 \pm \sqrt{22^{2} - 4 \cdot (8 \cdot 15)}}{2 \cdot 8}$

Step 3

Simplify.

Simplify the numerator.

Raise $22$ to the power of $2$ .

$x = \frac{- 22 \pm \sqrt{484 - 4 \cdot 8 \cdot 15}}{2 \cdot 8}$

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

Multiply $- 4$ by $8$ .

$x = \frac{- 22 \pm \sqrt{484 - 32 \cdot 15}}{2 \cdot 8}$

Multiply $- 32$ by $15$ .

$x = \frac{- 22 \pm \sqrt{484 - 480}}{2 \cdot 8}$

Subtract $480$ from $484$ .

$x = \frac{- 22 \pm \sqrt{4}}{2 \cdot 8}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 22 \pm \sqrt{2^{2}}}{2 \cdot 8}$

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

$x = \frac{- 22 \pm 2}{2 \cdot 8}$

Multiply $2$ by $8$ .

$x = \frac{- 22 \pm 2}{16}$

Simplify $\frac{- 22 \pm 2}{16}$ .

$x = \frac{- 11 \pm 1}{8}$

Step 4

The final answer is the combination of both solutions.

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