n(n+1)=1000

Solution for n(n+1)=1000 equation:

n(n+1)=1000

We move all terms to the left:

n(n+1)-(1000)=0

We multiply parentheses

n^2+n-1000=0

a = 1; b = 1; c = -1000;
Δ = b2-4ac
Δ = 12-4·1·(-1000)
Δ = 4001
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{4001}}{2*1}=\frac{-1-\sqrt{4001}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{4001}}{2*1}=\frac{-1+\sqrt{4001}}{2}
$