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

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

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 $a = 2$ , $b = - 1$ , and $c = - 5$ into the quadratic formula and solve for $x$ .

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

Step 3

Simplify.

Simplify the numerator.

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

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

Multiply $- 4 \cdot 2 \cdot - 5$ .

Multiply $- 4$ by $2$ .

$x = \frac{1 \pm \sqrt{1 - 8 \cdot - 5}}{2 \cdot 2}$

Multiply $- 8$ by $- 5$ .

$x = \frac{1 \pm \sqrt{1 + 40}}{2 \cdot 2}$

Add $1$ and $40$ .

$x = \frac{1 \pm \sqrt{41}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{1 \pm \sqrt{41}}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1 \pm \sqrt{41}}{4}$

Decimal Form:

$x = 1.85078105 \dots, - 1.35078105 \dots$