x(x+1)=4160

Solution for x(x+1)=4160 equation:

x(x+1)=4160

We move all terms to the left:

x(x+1)-(4160)=0

We multiply parentheses

x^2+x-4160=0

a = 1; b = 1; c = -4160;
Δ = b2-4ac
Δ = 12-4·1·(-4160)
Δ = 16641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16641}=129$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-129}{2*1}=\frac{-130}{2}
=-65
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+129}{2*1}=\frac{128}{2}
=64
$