56=n*(n-1)

Solution for 56=n*(n-1) equation:

56=n(n-1)

We move all terms to the left:

56-(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+56=0

We add all the numbers together, and all the variables

-1n^2+n+56=0

a = -1; b = 1; c = +56;
Δ = b2-4ac
Δ = 12-4·(-1)·56
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-15}{2*-1}=\frac{-16}{-2}
=+8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+15}{2*-1}=\frac{14}{-2}
=-7
$