6-4x=3x^2-6x+3

Solution for 6-4x=3x^2-6x+3 equation:

6-4x=3x^2-6x+3

We move all terms to the left:

6-4x-(3x^2-6x+3)=0

We get rid of parentheses

-3x^2-4x+6x-3+6=0

We add all the numbers together, and all the variables

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

a = -3; b = 2; c = +3;
Δ = b2-4ac
Δ = 22-4·(-3)·3
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{10}}{2*-3}=\frac{-2-2\sqrt{10}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{10}}{2*-3}=\frac{-2+2\sqrt{10}}{-6}
$