x(x+1)=16002

Solution for x(x+1)=16002 equation:

x(x+1)=16002

We move all terms to the left:

x(x+1)-(16002)=0

We multiply parentheses

x^2+x-16002=0

a = 1; b = 1; c = -16002;
Δ = b2-4ac
Δ = 12-4·1·(-16002)
Δ = 64009
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64009}=253$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-253}{2*1}=\frac{-254}{2}
=-127
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+253}{2*1}=\frac{252}{2}
=126
$