n(n+648000000)=2332800000000

Solution for n(n+648000000)=2332800000000 equation:

n(n+648000000)=2332800000000

We move all terms to the left:

n(n+648000000)-(2332800000000)=0

We multiply parentheses

n^2+648000000n-2332800000000=0

a = 1; b = 648000000; c = -2332800000000;
Δ = b2-4ac
Δ = 6480000002-4·1·(-2332800000000)
Δ = 419913331200000000
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:

$\sqrt{\Delta}=\sqrt{419913331200000000}=\sqrt{4665600000000*90002}=\sqrt{4665600000000}*\sqrt{90002}=2160000\sqrt{90002}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(648000000)-2160000\sqrt{90002}}{2*1}=\frac{-648000000-2160000\sqrt{90002}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(648000000)+2160000\sqrt{90002}}{2*1}=\frac{-648000000+2160000\sqrt{90002}}{2}
$