k(k+1)=110

Solution for k(k+1)=110 equation:

k(k+1)=110

We move all terms to the left:

k(k+1)-(110)=0

We multiply parentheses

k^2+k-110=0

a = 1; b = 1; c = -110;
Δ = b2-4ac
Δ = 12-4·1·(-110)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-21}{2*1}=\frac{-22}{2}
=-11
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+21}{2*1}=\frac{20}{2}
=10
$