-5x+x^2=2-2x-x^2

Solution for -5x+x^2=2-2x-x^2 equation:

-5x+x^2=2-2x-x^2

We move all terms to the left:

-5x+x^2-(2-2x-x^2)=0

We get rid of parentheses

x^2+x^2+2x-5x-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
$