We establish common fixed-point theorems for two self-mappings satisfying the (E.A) condition. The mappings are weakly compatible and include a point of coincidence in metric space. The mappings are satisfying contractive conditions defined by a category of implicit relations in six variables. Our theorems might be considered as extensions of the key results on b-metric space of Mohamed Akkouchi, common fixed-point theorems for 2 self-mappings of a b-metric space under an implicit relation, Hacettepe Journal of mathematics and statistics volume 40(6) (2011), 805-810 [1].