x(x+1)=65792

Solution for x(x+1)=65792 equation:

x(x+1)=65792

We move all terms to the left:

x(x+1)-(65792)=0

We multiply parentheses

x^2+x-65792=0

a = 1; b = 1; c = -65792;
Δ = b2-4ac
Δ = 12-4·1·(-65792)
Δ = 263169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{263169}=513$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-513}{2*1}=\frac{-514}{2}
=-257
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+513}{2*1}=\frac{512}{2}
=256
$