n=n*n+2n

Solution for n=n*n+2n equation:

n=n*n+2n

We move all terms to the left:

n-(n*n+2n)=0

We add all the numbers together, and all the variables

n-(+2n+n*n)=0

We get rid of parentheses

n-2n-n*n=0

We add all the numbers together, and all the variables

-1n-n*n=0

Wy multiply elements

-1n^2-1n=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:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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