9-6x=3x^2-12x+3

Solution for 9-6x=3x^2-12x+3 equation:

9-6x=3x^2-12x+3

We move all terms to the left:

9-6x-(3x^2-12x+3)=0

We get rid of parentheses

-3x^2-6x+12x-3+9=0

We add all the numbers together, and all the variables

-3x^2+6x+6=0

a = -3; b = 6; c = +6;
Δ = b2-4ac
Δ = 62-4·(-3)·6
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{3}}{2*-3}=\frac{-6-6\sqrt{3}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{3}}{2*-3}=\frac{-6+6\sqrt{3}}{-6}
$