-6x^2=12x-12

Solution for -6x^2=12x-12 equation:

-6x^2=12x-12

We move all terms to the left:

-6x^2-(12x-12)=0

We get rid of parentheses

-6x^2-12x+12=0

a = -6; b = -12; c = +12;
Δ = b2-4ac
Δ = -122-4·(-6)·12
Δ = 432
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{3}}{2*-6}=\frac{12-12\sqrt{3}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{3}}{2*-6}=\frac{12+12\sqrt{3}}{-12}
$