n(n+1)/2=741

Solution for n(n+1)/2=741 equation:

n(n+1)/2=741

We move all terms to the left:

n(n+1)/2-(741)=0

We multiply all the terms by the denominator


n(n+1)-741*2=0

We add all the numbers together, and all the variables

n(n+1)-1482=0

We multiply parentheses

n^2+n-1482=0

a = 1; b = 1; c = -1482;
Δ = b2-4ac
Δ = 12-4·1·(-1482)
Δ = 5929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5929}=77$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-77}{2*1}=\frac{-78}{2}
=-39
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+77}{2*1}=\frac{76}{2}
=38
$