2x-x^2=-x

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

2x-x^2=-x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+3x=0

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