H(x)=x2+2x

Solution for H(x)=x2+2x equation:

(H)=H2+2H

We move all terms to the left:

(H)-(H2+2H)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

-H^2-2H+H=0

We add all the numbers together, and all the variables

-1H^2-1H=0

a = -1; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-1)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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