y(2y-2)=12

Solution for y(2y-2)=12 equation:

y(2y-2)=12

We move all terms to the left:

y(2y-2)-(12)=0

We multiply parentheses

2y^2-2y-12=0

a = 2; b = -2; c = -12;
Δ = b2-4ac
Δ = -22-4·2·(-12)
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{-(-2)-10}{2*2}=\frac{-8}{4}
=-2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*2}=\frac{12}{4}
=3
$