Solve Using the Quadratic Formula 4x^2-7x-8=0

$4 x^{2} - 7 x - 8 = 0$

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 $a = 4$ , $b = - 7$ , and $c = - 8$ into the quadratic formula and solve for $x$ .

$\frac{7 \pm \sqrt{{(- 7)}^{2} - 4 \cdot (4 \cdot - 8)}}{2 \cdot 4}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 7$ to the power of $2$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot 4 \cdot - 8}}{2 \cdot 4}$

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

Multiply $- 4$ by $4$ .

$x = \frac{7 \pm \sqrt{49 - 16 \cdot - 8}}{2 \cdot 4}$

Multiply $- 16$ by $- 8$ .

$x = \frac{7 \pm \sqrt{49 + 128}}{2 \cdot 4}$

Add $49$ and $128$ .

$x = \frac{7 \pm \sqrt{177}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{7 \pm \sqrt{177}}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7 \pm \sqrt{177}}{8}$

Decimal Form:

$x = 2.53801683 \dots, - 0.78801683 \dots$