x=3x^2-9x+6

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

x=3x^2-9x+6

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2+10x-6=0

a = -3; b = 10; c = -6;
Δ = b2-4ac
Δ = 102-4·(-3)·(-6)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{7}}{2*-3}=\frac{-10-2\sqrt{7}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{7}}{2*-3}=\frac{-10+2\sqrt{7}}{-6}
$