k(k+1)=235.2

Solution for k(k+1)=235.2 equation:

k(k+1)=235.2

We move all terms to the left:

k(k+1)-(235.2)=0

We add all the numbers together, and all the variables

k(k+1)-235.2=0

We multiply parentheses

k^2+k-235.2=0

a = 1; b = 1; c = -235.2;
Δ = b2-4ac
Δ = 12-4·1·(-235.2)
Δ = 941.8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{941.8}}{2*1}=\frac{-1-\sqrt{941.8}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{941.8}}{2*1}=\frac{-1+\sqrt{941.8}}{2}
$