Solve Using the Quadratic Formula 2x^2-15x-2=0

$2 x^{2} - 15 x - 2 = 0$

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 $a = 2$ , $b = - 15$ , and $c = - 2$ into the quadratic formula and solve for $x$ .

$\frac{15 \pm \sqrt{{(- 15)}^{2} - 4 \cdot (2 \cdot - 2)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 15$ to the power of $2$ .

$x = \frac{15 \pm \sqrt{225 - 4 \cdot 2 \cdot - 2}}{2 \cdot 2}$

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

Multiply $- 4$ by $2$ .

$x = \frac{15 \pm \sqrt{225 - 8 \cdot - 2}}{2 \cdot 2}$

Multiply $- 8$ by $- 2$ .

$x = \frac{15 \pm \sqrt{225 + 16}}{2 \cdot 2}$

Add $225$ and $16$ .

$x = \frac{15 \pm \sqrt{241}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{15 \pm \sqrt{241}}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{15 \pm \sqrt{241}}{4}$

Decimal Form:

$x = 7.63104367 \dots, - 0.13104367 \dots$