(3x-2)(x-3)=3

Solution for (3x-2)(x-3)=3 equation:

(3x-2)(x-3)=3

We move all terms to the left:

(3x-2)(x-3)-(3)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-11x+3=0

a = 3; b = -11; c = +3;
Δ = b2-4ac
Δ = -112-4·3·3
Δ = 85
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{85}}{2*3}=\frac{11-\sqrt{85}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{85}}{2*3}=\frac{11+\sqrt{85}}{6}
$