420=n(n-1)

Solution for 420=n(n-1) equation:

420=n(n-1)

We move all terms to the left:

420-(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+420=0

We add all the numbers together, and all the variables

-1n^2+n+420=0

a = -1; b = 1; c = +420;
Δ = b2-4ac
Δ = 12-4·(-1)·420
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-41}{2*-1}=\frac{-42}{-2}
=+21
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+41}{2*-1}=\frac{40}{-2}
=-20
$