Let the probability of getting head for a biased coin be 1/4. It is tossed repeatedly until a head appears. Let N be the number of tosses required.…

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