n(n-1)/2=110

Solution for n(n-1)/2=110 equation:

n(n-1)/2=110

We move all terms to the left:

n(n-1)/2-(110)=0

We multiply all the terms by the denominator


n(n-1)-110*2=0

We add all the numbers together, and all the variables

n(n-1)-220=0

We multiply parentheses

n^2-1n-220=0

a = 1; b = -1; c = -220;
Δ = b2-4ac
Δ = -12-4·1·(-220)
Δ = 881
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{881}}{2*1}=\frac{1-\sqrt{881}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{881}}{2*1}=\frac{1+\sqrt{881}}{2}
$