n*(n-1)/2=6*5/2

Solution for n*(n-1)/2=6*5/2 equation:

n(n-1)/2=6*5/2

We move all terms to the left:

n(n-1)/2-(6*5/2)=0

We add all the numbers together, and all the variables

n(n-1)/2-3=0

We multiply all the terms by the denominator


n(n-1)-3*2=0

We add all the numbers together, and all the variables

n(n-1)-6=0

We multiply parentheses

n^2-1n-6=0

a = 1; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·1·(-6)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*1}=\frac{-4}{2}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*1}=\frac{6}{2}
=3
$