-2y(4y+1)=-8y-2

Solution for -2y(4y+1)=-8y-2 equation:

-2y(4y+1)=-8y-2

We move all terms to the left:

-2y(4y+1)-(-8y-2)=0

We multiply parentheses

-8y^2-2y-(-8y-2)=0

We get rid of parentheses

-8y^2-2y+8y+2=0

We add all the numbers together, and all the variables

-8y^2+6y+2=0

a = -8; b = 6; c = +2;
Δ = b2-4ac
Δ = 62-4·(-8)·2
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-10}{2*-8}=\frac{-16}{-16}
=1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10}{2*-8}=\frac{4}{-16}
=-1/4
$