n(n-1)/2=56

Solution for n(n-1)/2=56 equation:

n(n-1)/2=56

We move all terms to the left:

n(n-1)/2-(56)=0

We multiply all the terms by the denominator


n(n-1)-56*2=0

We add all the numbers together, and all the variables

n(n-1)-112=0

We multiply parentheses

n^2-1n-112=0

a = 1; b = -1; c = -112;
Δ = b2-4ac
Δ = -12-4·1·(-112)
Δ = 449
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{449}}{2*1}=\frac{1-\sqrt{449}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{449}}{2*1}=\frac{1+\sqrt{449}}{2}
$