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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -(x(-1x+1)), so:

x(-1x+1)

We multiply parentheses

-1x^2+x

Back to the equation:

-(-1x^2+x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-3x=0

a = 2; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·2·0
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{-(-3)-3}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*2}=\frac{6}{4}
=1+1/2
$