Mathematics Question from JEE Main 2023 · 11 April, Shift 2

Let the probability of getting a head for a biased coin be $\frac{1}{4}$. It is tossed repeatedly until a head appears. Let $N$ be the number of tosses required. If the probability that the equation $64x^2 + 5Nx + 1 = 0$ has no real root is $\frac{p}{q}$, where $p$ and $q$ are co-prime, then $q - p$ is equal to _____.