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.