How many years would it take for 75 percent of potassium to disintegrate?

Potassium has several radioactive isotopes with different half lives, but I presume you are thinking of K-40, the one used in potassium argon dating. Any isotope decays by half in one half life, so you'd need 2 half lives for 75% to decay. The half life of K-40 is 1.248 x 10^9 years, so the answer is 2.496 x 10^9 years.