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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses

2x-3x-(-1x+1)(x-3)-4+3=0

We multiply parentheses ..

-(-1x^2+3x+x-3)+2x-3x-4+3=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-5x+2=0

a = 1; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·1·2
Δ = 17
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{-(-5)-\sqrt{17}}{2*1}=\frac{5-\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{17}}{2*1}=\frac{5+\sqrt{17}}{2}
$