(n+1)*(n/2)=100

Solution for (n+1)*(n/2)=100 equation:

(n+1)(n/2)=100

We move all terms to the left:

(n+1)(n/2)-(100)=0

We add all the numbers together, and all the variables

(n+1)(+n/2)-100=0

We multiply parentheses ..

(+n^2+n)-100=0

We get rid of parentheses

n^2+n-100=0

a = 1; b = 1; c = -100;
Δ = b2-4ac
Δ = 12-4·1·(-100)
Δ = 401
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{401}}{2*1}=\frac{-1-\sqrt{401}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{401}}{2*1}=\frac{-1+\sqrt{401}}{2}
$