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

Solution for (x-2)(3x-2)+3x-2=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-5x+2=0

a = 3; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·3·2
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-1}{2*3}=\frac{4}{6}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*3}=\frac{6}{6}
=1
$