satisfiability is a canonical np-complete problem that requires to find a $0$-$1$ satisfying assignment for a given set of boolean constraints. i will consider the random walk algorithm that heuristically tries to find a solution by the random walk in the boolean hypercube, that converges to a satisfying assignment. i will prove the linear upper bound for the expected number of steps of the walk for the class of random small density $3$-sat formulas. this convergence follows the from geometric investigation of the convex hull of n randomly chosen points in the space.