1=14000n(n+1)

Solution for 1=14000n(n+1) equation:

1=14000n(n+1)

We move all terms to the left:

1-(14000n(n+1))=0


We calculate terms in parentheses: -(14000n(n+1)), so:

14000n(n+1)

We multiply parentheses

14000n^2+14000n

Back to the equation:

-(14000n^2+14000n)


We get rid of parentheses

-14000n^2-14000n+1=0

a = -14000; b = -14000; c = +1;
Δ = b2-4ac
Δ = -140002-4·(-14000)·1
Δ = 196056000
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:

$\sqrt{\Delta}=\sqrt{196056000}=\sqrt{14400*13615}=\sqrt{14400}*\sqrt{13615}=120\sqrt{13615}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14000)-120\sqrt{13615}}{2*-14000}=\frac{14000-120\sqrt{13615}}{-28000}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14000)+120\sqrt{13615}}{2*-14000}=\frac{14000+120\sqrt{13615}}{-28000}
$