x(x+1)=6642

Solution for x(x+1)=6642 equation:

x(x+1)=6642

We move all terms to the left:

x(x+1)-(6642)=0

We multiply parentheses

x^2+x-6642=0

a = 1; b = 1; c = -6642;
Δ = b2-4ac
Δ = 12-4·1·(-6642)
Δ = 26569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{26569}=163$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-163}{2*1}=\frac{-164}{2}
=-82
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+163}{2*1}=\frac{162}{2}
=81
$