Solve Using the Quadratic Formula 5x^2-4x-7=0

$5 x^{2} - 4 x - 7 = 0$

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 $a = 5$ , $b = - 4$ , and $c = - 7$ into the quadratic formula and solve for $x$ .

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

Step 3

Simplify.

Simplify the numerator.

Raise $- 4$ to the power of $2$ .

$x = \frac{4 \pm \sqrt{16 - 4 \cdot 5 \cdot - 7}}{2 \cdot 5}$

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

Multiply $- 4$ by $5$ .

$x = \frac{4 \pm \sqrt{16 - 20 \cdot - 7}}{2 \cdot 5}$

Multiply $- 20$ by $- 7$ .

$x = \frac{4 \pm \sqrt{16 + 140}}{2 \cdot 5}$

Add $16$ and $140$ .

$x = \frac{4 \pm \sqrt{156}}{2 \cdot 5}$

Rewrite $156$ as $2^{2} \cdot 39$ .

Factor $4$ out of $156$ .

$x = \frac{4 \pm \sqrt{4 (39)}}{2 \cdot 5}$

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

$x = \frac{4 \pm \sqrt{2^{2} \cdot 39}}{2 \cdot 5}$

Pull terms out from under the radical.

$x = \frac{4 \pm 2 \sqrt{39}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{4 \pm 2 \sqrt{39}}{10}$

Simplify $\frac{4 \pm 2 \sqrt{39}}{10}$ .

$x = \frac{2 \pm \sqrt{39}}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2 \pm \sqrt{39}}{5}$

Decimal Form:

$x = 1.64899959 \dots, - 0.84899959 \dots$