12=2w^2+2w

Solution for 12=2w^2+2w equation:

12=2w^2+2w

We move all terms to the left:

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

We get rid of parentheses

-2w^2-2w+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:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*-2}=\frac{-8}{-4}
=+2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*-2}=\frac{12}{-4}
=-3
$