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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x^2-11x+9=0

a = 3; b = -11; c = +9;
Δ = b2-4ac
Δ = -112-4·3·9
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{13}}{2*3}=\frac{11-\sqrt{13}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{13}}{2*3}=\frac{11+\sqrt{13}}{6}
$