57=n(n-1)

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

57=n(n-1)

We move all terms to the left:

57-(n(n-1))=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 get rid of parentheses

-n^2+1n+57=0

We add all the numbers together, and all the variables

-1n^2+n+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}
$