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

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

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 $c = - 5$ into the quadratic formula and solve for $x$ .

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

Step 3

Simplify.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $5$ .

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

Multiply $- 20$ by $- 5$ .

$x = \frac{- 4 \pm \sqrt{16 + 100}}{2 \cdot 5}$

Add $16$ and $100$ .

$x = \frac{- 4 \pm \sqrt{116}}{2 \cdot 5}$

Rewrite $116$ as $2^{2} \cdot 29$ .

Factor $4$ out of $116$ .

$x = \frac{- 4 \pm \sqrt{4 (29)}}{2 \cdot 5}$

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

$x = \frac{- 4 \pm \sqrt{2^{2} \cdot 29}}{2 \cdot 5}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm 2 \sqrt{29}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{- 4 \pm 2 \sqrt{29}}{10}$

Simplify $\frac{- 4 \pm 2 \sqrt{29}}{10}$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.67703296 \dots, - 1.47703296 \dots$