x(x-2)=3x-x2

Solution for x(x-2)=3x-x2 equation:

x(x-2)=3x-x2

We move all terms to the left:

x(x-2)-(3x-x2)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-5x=0

a = 2; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·2·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*2}=\frac{10}{4}
=2+1/2
$