(n(n-1))/2=36

Solution for (n(n-1))/2=36 equation:

(n(n-1))/2=36

We move all terms to the left:

(n(n-1))/2-(36)=0

We multiply all the terms by the denominator


(n(n-1))-36*2=0


We calculate terms in parentheses: +(n(n-1)), so:

n(n-1)

We multiply parentheses

n^2-1n

Back to the equation:

+(n^2-1n)


We add all the numbers together, and all the variables

(n^2-1n)-72=0

We get rid of parentheses

n^2-1n-72=0

a = 1; b = -1; c = -72;
Δ = b2-4ac
Δ = -12-4·1·(-72)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-17}{2*1}=\frac{-16}{2}
=-8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+17}{2*1}=\frac{18}{2}
=9
$