Solve Using the Quadratic Formula 5x^2-13x+7=0

$5 x^{2} - 13 x + 7 = 0$

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 $c = 7$ into the quadratic formula and solve for $x$ .

$\frac{13 \pm \sqrt{{(- 13)}^{2} - 4 \cdot (5 \cdot 7)}}{2 \cdot 5}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{13 \pm \sqrt{169 - 4 \cdot 5 \cdot 7}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot 7$ .

Multiply $- 4$ by $5$ .

$x = \frac{13 \pm \sqrt{169 - 20 \cdot 7}}{2 \cdot 5}$

Multiply $- 20$ by $7$ .

$x = \frac{13 \pm \sqrt{169 - 140}}{2 \cdot 5}$

Subtract $140$ from $169$ .

$x = \frac{13 \pm \sqrt{29}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{13 \pm \sqrt{29}}{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{13 \pm \sqrt{29}}{10}$

Decimal Form:

$x = 1.83851648 \dots, 0.76148351 \dots$