n*(n+1)=720

Solution for n*(n+1)=720 equation:

n(n+1)=720

We move all terms to the left:

n(n+1)-(720)=0

We multiply parentheses

n^2+n-720=0

a = 1; b = 1; c = -720;
Δ = b2-4ac
Δ = 12-4·1·(-720)
Δ = 2881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{2881}}{2*1}=\frac{-1-\sqrt{2881}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{2881}}{2*1}=\frac{-1+\sqrt{2881}}{2}
$