Solve Using the Quadratic Formula 5x^2-2x-6=0

$5 x^{2} - 2 x - 6 = 0$

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 $a = 5$ , $b = - 2$ , and $c = - 6$ into the quadratic formula and solve for $x$ .

$\frac{2 \pm \sqrt{{(- 2)}^{2} - 4 \cdot (5 \cdot - 6)}}{2 \cdot 5}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{2 \pm \sqrt{4 - 4 \cdot 5 \cdot - 6}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot - 6$ .

Multiply $- 4$ by $5$ .

$x = \frac{2 \pm \sqrt{4 - 20 \cdot - 6}}{2 \cdot 5}$

Multiply $- 20$ by $- 6$ .

$x = \frac{2 \pm \sqrt{4 + 120}}{2 \cdot 5}$

Add $4$ and $120$ .

$x = \frac{2 \pm \sqrt{124}}{2 \cdot 5}$

Rewrite $124$ as $2^{2} \cdot 31$ .

Factor $4$ out of $124$ .

$x = \frac{2 \pm \sqrt{4 (31)}}{2 \cdot 5}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{2 \pm \sqrt{2^{2} \cdot 31}}{2 \cdot 5}$

Pull terms out from under the radical.

$x = \frac{2 \pm 2 \sqrt{31}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{2 \pm 2 \sqrt{31}}{10}$

Simplify $\frac{2 \pm 2 \sqrt{31}}{10}$ .

$x = \frac{1 \pm \sqrt{31}}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1 \pm \sqrt{31}}{5}$

Decimal Form:

$x = 1.31355287 \dots, - 0.91355287 \dots$