Solve Using the Quadratic Formula 5x^2-8x+2=0

$5 x^{2} - 8 x + 2 = 0$

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 $a = 5$ , $b = - 8$ , and $c = 2$ into the quadratic formula and solve for $x$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (5 \cdot 2)}}{2 \cdot 5}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 5 \cdot 2}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot 2$ .

Multiply $- 4$ by $5$ .

$x = \frac{8 \pm \sqrt{64 - 20 \cdot 2}}{2 \cdot 5}$

Multiply $- 20$ by $2$ .

$x = \frac{8 \pm \sqrt{64 - 40}}{2 \cdot 5}$

Subtract $40$ from $64$ .

$x = \frac{8 \pm \sqrt{24}}{2 \cdot 5}$

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$x = \frac{8 \pm \sqrt{4 (6)}}{2 \cdot 5}$

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

$x = \frac{8 \pm \sqrt{2^{2} \cdot 6}}{2 \cdot 5}$

Pull terms out from under the radical.

$x = \frac{8 \pm 2 \sqrt{6}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{8 \pm 2 \sqrt{6}}{10}$

Simplify $\frac{8 \pm 2 \sqrt{6}}{10}$ .

$x = \frac{4 \pm \sqrt{6}}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4 \pm \sqrt{6}}{5}$

Decimal Form:

$x = 1.28989794 \dots, 0.31010205 \dots$