-4y^2+1=-2y

Solution for -4y^2+1=-2y equation:

-4y^2+1=-2y

We move all terms to the left:

-4y^2+1-(-2y)=0

We get rid of parentheses

-4y^2+2y+1=0

a = -4; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-4)·1
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{5}}{2*-4}=\frac{-2-2\sqrt{5}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{5}}{2*-4}=\frac{-2+2\sqrt{5}}{-8}
$