n(n-1)/2=2926

Solution for n(n-1)/2=2926 equation:

n(n-1)/2=2926

We move all terms to the left:

n(n-1)/2-(2926)=0

We multiply all the terms by the denominator


n(n-1)-2926*2=0

We add all the numbers together, and all the variables

n(n-1)-5852=0

We multiply parentheses

n^2-1n-5852=0

a = 1; b = -1; c = -5852;
Δ = b2-4ac
Δ = -12-4·1·(-5852)
Δ = 23409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{23409}=153$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-153}{2*1}=\frac{-152}{2}
=-76
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+153}{2*1}=\frac{154}{2}
=77
$