negative binomial distribution question

In some experiment(with independent trials, and two results, success and no-success), we continue until the next relation be true:

c1*N°success-c2*N°no-success > c3 , with c1,c2,c3=constant>0

a) What is the probability the relation above be true in some moment, if we can do the experiment up to n trials? The probabilty of success is p.

b) How many trials we should do, if we want the above relation be true with at least 80% confidence?

Thanks for your answers!