We consider the regular balanced model of satisfiability formula generation in conjunctive normal form (CNF), where each literal participates in equal number of clauses and there are k literals participating in a clause. We say that a formula is p-satisfying if there is a truth assignment satisfying 1 - 2-k + p2- fraction of clauses. Using the first moment method we determine upper bound on the threshold clause density such that there are no p-satisfying assignments with high probability above this upper bound. There are two aspects in deriving the lower bound using the second moment method. The first aspect is, given any p ∈ (0,1) and k, evaluate the lower bound on the threshold. This evaluation is numerical in nature. The second aspect is to derive the lower bound as a function of p for large enough k. We address the first aspect and evaluate the lower bound on the p-satisfying threshold using the second moment method. Based on the numerical evaluation, we observe that as k increases the ratio of the lower bound and the upper bound seems to converge to one.