Solve Using the Quadratic Formula 8x^2+9x-4=0

$8 x^{2} + 9 x - 4 = 0$

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 $a = 8$ , $b = 9$ , and $c = - 4$ into the quadratic formula and solve for $x$ .

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

Step 3

Simplify.

Simplify the numerator.

Raise $9$ to the power of $2$ .

$x = \frac{- 9 \pm \sqrt{81 - 4 \cdot 8 \cdot - 4}}{2 \cdot 8}$

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

Multiply $- 4$ by $8$ .

$x = \frac{- 9 \pm \sqrt{81 - 32 \cdot - 4}}{2 \cdot 8}$

Multiply $- 32$ by $- 4$ .

$x = \frac{- 9 \pm \sqrt{81 + 128}}{2 \cdot 8}$

Add $81$ and $128$ .

$x = \frac{- 9 \pm \sqrt{209}}{2 \cdot 8}$

Multiply $2$ by $8$ .

$x = \frac{- 9 \pm \sqrt{209}}{16}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 9 \pm \sqrt{209}}{16}$

Decimal Form:

$x = 0.34105201 \dots, - 1.46605201 \dots$