6x^2=-6x+12

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

6x^2=-6x+12

We move all terms to the left:

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

We get rid of parentheses

6x^2+6x-12=0

a = 6; b = 6; c = -12;
Δ = b2-4ac
Δ = 62-4·6·(-12)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18}{2*6}=\frac{-24}{12}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18}{2*6}=\frac{12}{12}
=1
$