n*(n-1)=57

Solution for n*(n-1)=57 equation:

n(n-1)=57

We move all terms to the left:

n(n-1)-(57)=0

We multiply parentheses

n^2-1n-57=0

a = 1; b = -1; c = -57;
Δ = b2-4ac
Δ = -12-4·1·(-57)
Δ = 229
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{229}}{2*1}=\frac{1-\sqrt{229}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{229}}{2*1}=\frac{1+\sqrt{229}}{2}
$