The roots of the equation $2x^2 - 5x - 4 = 0$ can be written in the form $x = \frac{m \pm \sqrt{n}}{p}$, where $m$, $n$, and $p$ are positive integers with a greatest common divisor of 1. What is the value of $n$?

By the quadratic formula,

\[x = \frac{5 \pm \sqrt{61}}{4},\]

so $n = 61$.