I recently asked this very similar question on how Grovers algorithm must be modified in order to solve 3-SAT and learned that it actually needs no modification at all.
However, what I still don't get is how to determine whether a satisfying variable assignment was found after having applied Grover's algorithm. The final step (as described in wikipedia) is to measure $λ_ω$ which in the case of solving 3-SAT would give me an assignment for the variables of my formula. Do I need to check manually whether this assignment is indeed a satisfying assignment? Or is there any better way to find out whether there exists at least one match?