12y^2=2-2y

Solution for 12y^2=2-2y equation:

12y^2=2-2y

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

12y^2+2y-2=0

a = 12; b = 2; c = -2;
Δ = b2-4ac
Δ = 22-4·12·(-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{-(2)-10}{2*12}=\frac{-12}{24}
=-1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*12}=\frac{8}{24}
=1/3
$