Solve Using the Quadratic Formula 5x^2-13x-17=0

$5 x^{2} - 13 x - 17 = 0$

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 $a = 5$ , $b = - 13$ , and $c = - 17$ into the quadratic formula and solve for $x$ .

$\frac{13 \pm \sqrt{{(- 13)}^{2} - 4 \cdot (5 \cdot - 17)}}{2 \cdot 5}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 13$ to the power of $2$ .

$x = \frac{13 \pm \sqrt{169 - 4 \cdot 5 \cdot - 17}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot - 17$ .

Multiply $- 4$ by $5$ .

$x = \frac{13 \pm \sqrt{169 - 20 \cdot - 17}}{2 \cdot 5}$

Multiply $- 20$ by $- 17$ .

$x = \frac{13 \pm \sqrt{169 + 340}}{2 \cdot 5}$

Add $169$ and $340$ .

$x = \frac{13 \pm \sqrt{509}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{13 \pm \sqrt{509}}{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{13 \pm \sqrt{509}}{10}$

Decimal Form:

$x = 3.55610283 \dots, - 0.95610283 \dots$