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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-5x+2=0

a = 2; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·2·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*2}=\frac{2}{4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*2}=\frac{8}{4}
=2
$