2n(n+1)=n

Solution for 2n(n+1)=n equation:

2n(n+1)=n

We move all terms to the left:

2n(n+1)-(n)=0

We add all the numbers together, and all the variables

-1n+2n(n+1)=0

We multiply parentheses

2n^2-1n+2n=0

We add all the numbers together, and all the variables

2n^2+n=0

a = 2; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·2·0
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*2}=\frac{-2}{4}
=-1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*2}=\frac{0}{4}
=0
$