2(3y-2)y=2

Solution for 2(3y-2)y=2 equation:

2(3y-2)y=2

We move all terms to the left:

2(3y-2)y-(2)=0

We multiply parentheses

6y^2-4y-2=0

a = 6; b = -4; c = -2;
Δ = b2-4ac
Δ = -42-4·6·(-2)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*6}=\frac{-4}{12}
=-1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*6}=\frac{12}{12}
=1
$