5y2=2y+2

Solution for 5y2=2y+2 equation:

5y^2=2y+2

We move all terms to the left:

5y^2-(2y+2)=0

We get rid of parentheses

5y^2-2y-2=0

a = 5; b = -2; c = -2;
Δ = b2-4ac
Δ = -22-4·5·(-2)
Δ = 44
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{11}}{2*5}=\frac{2-2\sqrt{11}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{11}}{2*5}=\frac{2+2\sqrt{11}}{10}
$