Given probability find the number of times an experiment is repeated? Binomial probability

I have the probability (p1) that the number of successes in a repeated experiment (binomial probability n- repetitions) is at least K .I also have the probability of success in a single experiment (p).
P(X>K)=p1;
The problem is to find N ( the number of repetitions)
(binomial probability P(X=k)= binomCoef(n,k)*p^k * (1-p)^(k-n) for n-repetitions with k successes;)

idk of an exact analytical way to solve this
you can use trial & error using a binomial calculator if an exact answers is needed,

or use the normal approximation to the binomial
find z-score for cumulative probability for p1 = z (say)
mean = np
SD = sqrt(npq)

solve (p1-np)/SD = z
ie (p1-np)^2 = z^2*npq, a quadratic in n