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

Solution for 2x(x-1)-3(x-1)=0 equation:

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

We multiply parentheses

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

We add all the numbers together, and all the variables

2x^2-5x+3=0

a = 2; b = -5; c = +3;
Δ = b2-4ac
Δ = -52-4·2·3
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*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*2}=\frac{6}{4}
=1+1/2
$