1122=n(n+1)

Solution for 1122=n(n+1) equation:

1122=n(n+1)

We move all terms to the left:

1122-(n(n+1))=0


We calculate terms in parentheses: -(n(n+1)), so:

n(n+1)

We multiply parentheses

n^2+n

Back to the equation:

-(n^2+n)


We get rid of parentheses

-n^2-n+1122=0

We add all the numbers together, and all the variables

-1n^2-1n+1122=0

a = -1; b = -1; c = +1122;
Δ = b2-4ac
Δ = -12-4·(-1)·1122
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-67}{2*-1}=\frac{-66}{-2}
=+33
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+67}{2*-1}=\frac{68}{-2}
=-34
$