Solve Using the Quadratic Formula 5y^2-8y=2

$5 y^{2} - 8 y = 2$

Step 1

Subtract $2$ from both sides of the equation.

$5 y^{2} - 8 y - 2 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

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

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

Step 4

Simplify.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $5$ .

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

Multiply $- 20$ by $- 2$ .

$y = \frac{8 \pm \sqrt{64 + 40}}{2 \cdot 5}$

Add $64$ and $40$ .

$y = \frac{8 \pm \sqrt{104}}{2 \cdot 5}$

Rewrite $104$ as $2^{2} \cdot 26$ .

Factor $4$ out of $104$ .

$y = \frac{8 \pm \sqrt{4 (26)}}{2 \cdot 5}$

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

$y = \frac{8 \pm \sqrt{2^{2} \cdot 26}}{2 \cdot 5}$

Pull terms out from under the radical.

$y = \frac{8 \pm 2 \sqrt{26}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$y = \frac{8 \pm 2 \sqrt{26}}{10}$

Simplify $\frac{8 \pm 2 \sqrt{26}}{10}$ .

$y = \frac{4 \pm \sqrt{26}}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{4 \pm \sqrt{26}}{5}$

Decimal Form:

$y = 1.81980390 \dots, - 0.21980390 \dots$