4(y-2)y=2

Solution for 4(y-2)y=2 equation:

4(y-2)y=2

We move all terms to the left:

4(y-2)y-(2)=0

We multiply parentheses

4y^2-8y-2=0

a = 4; b = -8; c = -2;
Δ = b2-4ac
Δ = -82-4·4·(-2)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{6}}{2*4}=\frac{8-4\sqrt{6}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{6}}{2*4}=\frac{8+4\sqrt{6}}{8}
$