n(n+1)/2=44

Solution for n(n+1)/2=44 equation:

n(n+1)/2=44

We move all terms to the left:

n(n+1)/2-(44)=0

We multiply all the terms by the denominator


n(n+1)-44*2=0

We add all the numbers together, and all the variables

n(n+1)-88=0

We multiply parentheses

n^2+n-88=0

a = 1; b = 1; c = -88;
Δ = b2-4ac
Δ = 12-4·1·(-88)
Δ = 353
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{353}}{2*1}=\frac{-1-\sqrt{353}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{353}}{2*1}=\frac{-1+\sqrt{353}}{2}
$