6480=n+n^2

Solution for 6480=n+n^2 equation:

6480=n+n^2

We move all terms to the left:

6480-(n+n^2)=0

We get rid of parentheses

-n^2-n+6480=0

We add all the numbers together, and all the variables

-1n^2-1n+6480=0

a = -1; b = -1; c = +6480;
Δ = b2-4ac
Δ = -12-4·(-1)·6480
Δ = 25921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25921}=161$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-161}{2*-1}=\frac{-160}{-2}
=+80
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+161}{2*-1}=\frac{162}{-2}
=-81
$