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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We add all the numbers together, and all the variables

-1x^2-1x=0

a = -1; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-1)·0
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{-(-1)-1}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-1}=\frac{2}{-2}
=-1
$