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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-3x-2=0

a = 2; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·2·(-2)
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{-(-3)-5}{2*2}=\frac{-2}{4}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5}{2*2}=\frac{8}{4}
=2
$