n*(n+1)=276*2

Solution for n*(n+1)=276*2 equation:

n(n+1)=276*2

We move all terms to the left:

n(n+1)-(276*2)=0

We add all the numbers together, and all the variables

n(n+1)-552=0

We multiply parentheses

n^2+n-552=0

a = 1; b = 1; c = -552;
Δ = b2-4ac
Δ = 12-4·1·(-552)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-47}{2*1}=\frac{-48}{2}
=-24
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+47}{2*1}=\frac{46}{2}
=23
$