x(x+1)=2000

Solution for x(x+1)=2000 equation:

x(x+1)=2000

We move all terms to the left:

x(x+1)-(2000)=0

We multiply parentheses

x^2+x-2000=0

a = 1; b = 1; c = -2000;
Δ = b2-4ac
Δ = 12-4·1·(-2000)
Δ = 8001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8001}=\sqrt{9*889}=\sqrt{9}*\sqrt{889}=3\sqrt{889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{889}}{2*1}=\frac{-1-3\sqrt{889}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{889}}{2*1}=\frac{-1+3\sqrt{889}}{2}
$