Counting Candles - Math Problem

A girl says she has blown out 136 birthday candles in her life. You are given the challenge of determining her age.

You figure out she's 16. The simplest way to solve this is to count 1+2+3+... until the sum of the values equals the total. But what's a more efficient way to derive the answer?

If x is the total, and n is the age of the person, we will see:

2x = n^2 + n

So we know that: n ~ sqrt (2x)

It's been a while since basic trigonometry, would you have to write the equation like this?

f(x) = 1/2(n + 0)(n + 1)

I can't remember how to break it down.