Solve Using the Quadratic Formula 8x^2-6x-9=0

$8 x^{2} - 6 x - 9 = 0$

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 $a = 8$ , $b = - 6$ , and $c = - 9$ into the quadratic formula and solve for $x$ .

$\frac{6 \pm \sqrt{{(- 6)}^{2} - 4 \cdot (8 \cdot - 9)}}{2 \cdot 8}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 6$ to the power of $2$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 8 \cdot - 9}}{2 \cdot 8}$

Multiply $- 4 \cdot 8 \cdot - 9$ .

Multiply $- 4$ by $8$ .

$x = \frac{6 \pm \sqrt{36 - 32 \cdot - 9}}{2 \cdot 8}$

Multiply $- 32$ by $- 9$ .

$x = \frac{6 \pm \sqrt{36 + 288}}{2 \cdot 8}$

Add $36$ and $288$ .

$x = \frac{6 \pm \sqrt{324}}{2 \cdot 8}$

Rewrite $324$ as $18^{2}$ .

$x = \frac{6 \pm \sqrt{18^{2}}}{2 \cdot 8}$

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

$x = \frac{6 \pm 18}{2 \cdot 8}$

Multiply $2$ by $8$ .

$x = \frac{6 \pm 18}{16}$

Simplify $\frac{6 \pm 18}{16}$ .

$x = \frac{3 \pm 9}{8}$

Step 4

The final answer is the combination of both solutions.

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