-2x=2x^2-12

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

-2x=2x^2-12

We move all terms to the left:

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

We get rid of parentheses

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

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