n(1440n-2880)=360

Solution for n(1440n-2880)=360 equation:

n(1440n-2880)=360

We move all terms to the left:

n(1440n-2880)-(360)=0

We multiply parentheses

1440n^2-2880n-360=0

a = 1440; b = -2880; c = -360;
Δ = b2-4ac
Δ = -28802-4·1440·(-360)
Δ = 10368000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10368000}=\sqrt{2073600*5}=\sqrt{2073600}*\sqrt{5}=1440\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2880)-1440\sqrt{5}}{2*1440}=\frac{2880-1440\sqrt{5}}{2880}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2880)+1440\sqrt{5}}{2*1440}=\frac{2880+1440\sqrt{5}}{2880}
$