182=n(n+1)

Solution for 182=n(n+1) equation:

182=n(n+1)

We move all terms to the left:

182-(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+182=0

We add all the numbers together, and all the variables

-1n^2-1n+182=0

a = -1; b = -1; c = +182;
Δ = b2-4ac
Δ = -12-4·(-1)·182
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-27}{2*-1}=\frac{-26}{-2}
=+13
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+27}{2*-1}=\frac{28}{-2}
=-14
$