Solve Using the Quadratic Formula 4x^2-x-5=0

$4 x^{2} - x - 5 = 0$

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 $a = 4$ , $b = - 1$ , and $c = - 5$ into the quadratic formula and solve for $x$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (4 \cdot - 5)}}{2 \cdot 4}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 1$ to the power of $2$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot 4 \cdot - 5}}{2 \cdot 4}$

Multiply $- 4 \cdot 4 \cdot - 5$ .

Multiply $- 4$ by $4$ .

$x = \frac{1 \pm \sqrt{1 - 16 \cdot - 5}}{2 \cdot 4}$

Multiply $- 16$ by $- 5$ .

$x = \frac{1 \pm \sqrt{1 + 80}}{2 \cdot 4}$

Add $1$ and $80$ .

$x = \frac{1 \pm \sqrt{81}}{2 \cdot 4}$

Rewrite $81$ as $9^{2}$ .

$x = \frac{1 \pm \sqrt{9^{2}}}{2 \cdot 4}$

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

$x = \frac{1 \pm 9}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{1 \pm 9}{8}$

Step 4

The final answer is the combination of both solutions.

$x = \frac{5}{4}, - 1$