Y=2x+x2

Solution for Y=2x+x2 equation:

=2Y+Y2

We move all terms to the left:

-(2Y+Y2)=0

We add all the numbers together, and all the variables

-(+2Y+Y^2)=0

We get rid of parentheses

-Y^2-2Y=0

We add all the numbers together, and all the variables

-1Y^2-2Y=0

a = -1; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-1)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-1}=\frac{0}{-2}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-1}=\frac{4}{-2}
=-2
$