24864=n^2-n

Solution for 24864=n^2-n equation:

24864=n^2-n

We move all terms to the left:

24864-(n^2-n)=0

We get rid of parentheses

-n^2+n+24864=0

We add all the numbers together, and all the variables

-1n^2+n+24864=0

a = -1; b = 1; c = +24864;
Δ = b2-4ac
Δ = 12-4·(-1)·24864
Δ = 99457
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{99457}}{2*-1}=\frac{-1-\sqrt{99457}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{99457}}{2*-1}=\frac{-1+\sqrt{99457}}{-2}
$