-5y^2+2y+1=0

Solution for -5y^2+2y+1=0 equation:

-5y^2+2y+1=0

a = -5; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-5)·1
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{6}}{2*-5}=\frac{-2-2\sqrt{6}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{6}}{2*-5}=\frac{-2+2\sqrt{6}}{-10}
$