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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-4x^2+5x-1=0

a = -4; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·(-4)·(-1)
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*-4}=\frac{-8}{-8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3}{2*-4}=\frac{-2}{-8}
=1/4
$