(2x-1)(3x-3)=1

Solution for (2x-1)(3x-3)=1 equation:

(2x-1)(3x-3)=1

We move all terms to the left:

(2x-1)(3x-3)-(1)=0

We multiply parentheses ..

(+6x^2-6x-3x+3)-1=0

We get rid of parentheses

6x^2-6x-3x+3-1=0

We add all the numbers together, and all the variables

6x^2-9x+2=0

a = 6; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·6·2
Δ = 33
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{-(-9)-\sqrt{33}}{2*6}=\frac{9-\sqrt{33}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{33}}{2*6}=\frac{9+\sqrt{33}}{12}
$