A random variable $X$ is normally distributed with mean $\mu$. With a probability of $\frac{1}{2}$, the equation $y^2 + 2y + X < 0$ where $y$ is known to have a single real root. What is the value of $\mu$?
This is the question out of my workbook. My problem here is that I'm not sure what to do with that equation, what it means, or how to find the mean with it? I'm less interested in the actual answer than I am how to find it.