Probability

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