I was solving a 2 egg dropping problem, which looks like http://datagenetics.com/blog/july22012/index.html.

Problem Definition

You are given two eggs, and access to a 100-storey building. Both eggs are identical. The aim is to find out the highest floor from which an egg will not break when dropped out of a window from that floor. If an egg is dropped and does not break, it is undamaged and can be dropped again. However, once an egg is broken, that’s it for that egg.

If an egg breaks when dropped from floor n, then it would also have broken from any floor above that. If an egg survives a fall, then it will survive any fall shorter than that.

The question is: What strategy should you adopt to minimize the number egg drops it takes to find the solution?. (And what is the worst case for the number of drops it will take?)

Proposed solution

The solution in the link says I can use a qudratic inequality like: n^2 + n - 200 >= 0 to get the first floor to drop the egg, and hence the worst number of cases.

Issue with solution that needs help

However, I have a problem with chosing the right root here. As we have a positve and a negative root, which one should I select ? For example, for 100, this works okey with selecting 13.65 ~ to 14, but say for 17, we have 5.352349 and -6.35234. How do I know that 6 is the one here ?