Solve Using the Quadratic Formula 5x^2-13x-6=0

$5 x^{2} - 13 x - 6 = 0$

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 $a = 5$ , $b = - 13$ , and $c = - 6$ into the quadratic formula and solve for $x$ .

$\frac{13 \pm \sqrt{{(- 13)}^{2} - 4 \cdot (5 \cdot - 6)}}{2 \cdot 5}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{13 \pm \sqrt{169 - 4 \cdot 5 \cdot - 6}}{2 \cdot 5}$

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

Multiply $- 4$ by $5$ .

$x = \frac{13 \pm \sqrt{169 - 20 \cdot - 6}}{2 \cdot 5}$

Multiply $- 20$ by $- 6$ .

$x = \frac{13 \pm \sqrt{169 + 120}}{2 \cdot 5}$

Add $169$ and $120$ .

$x = \frac{13 \pm \sqrt{289}}{2 \cdot 5}$

Rewrite $289$ as $17^{2}$ .

$x = \frac{13 \pm \sqrt{17^{2}}}{2 \cdot 5}$

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

$x = \frac{13 \pm 17}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{13 \pm 17}{10}$

Step 4

The final answer is the combination of both solutions.

$x = 3, - \frac{2}{5}$