Solve for y 5y^2+7y-1=0

$5 y^{2} + 7 y - 1 = 0$

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 $a = 5$ , $b = 7$ , and $c = - 1$ into the quadratic formula and solve for $y$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (5 \cdot - 1)}}{2 \cdot 5}$

Step 3

Simplify.

Simplify the numerator.

Raise $7$ to the power of $2$ .

$y = \frac{- 7 \pm \sqrt{49 - 4 \cdot 5 \cdot - 1}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot - 1$ .

Multiply $- 4$ by $5$ .

$y = \frac{- 7 \pm \sqrt{49 - 20 \cdot - 1}}{2 \cdot 5}$

Multiply $- 20$ by $- 1$ .

$y = \frac{- 7 \pm \sqrt{49 + 20}}{2 \cdot 5}$

Add $49$ and $20$ .

$y = \frac{- 7 \pm \sqrt{69}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$y = \frac{- 7 \pm \sqrt{69}}{10}$

Step 4

The final answer is the combination of both solutions.

$y = - \frac{7 - \sqrt{69}}{10}, - \frac{7 + \sqrt{69}}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{7 - \sqrt{69}}{10}, - \frac{7 + \sqrt{69}}{10}$

Decimal Form:

$y = 0.13066238 \dots, - 1.53066238 \dots$