Mobile-edge computing (MEC) is a new paradigm with a great potential to extend mobile users capabilities becauseof its proximity. It can contribute efficiently to optimize the energy consumption to preserve privacy, and reduce the bottlenecks of the network traffic. In addition, intensive-computation offloading is an active research area that can lessen latencies and energy consumption. Nevertheless, within multiuser networks with a multi-task scenario, select the tasks to offload is complex and critical. Actually, these selections and the resources' allocation have to be carefully considered as they affect the resulting energies and delays. In this work, we study a scenario considering a user-adaptive offloading where each user runs a list of heavy computation-tasks. Every task has to be processed in its associated MEC server within a fixed deadline. Hence, the proposed optimization problem target the minimization of a weighted-sum normalized function depending on three metrics. The first is energy consumption, the second is the total processing delays, and the third is the unsatisfied processing workload. The solution of the general problem is obtained using the solutions of two sub-problems. Also, all solutions are evaluated using a set of simulation experiments. Finally, the execution times are very encouraging for moderate sizes, and the proposed heuristic solutions give satisfactory results in terms of users cost function in pseudo-polynomial times.