A random-bond Blume-Capel model is proposed in order to study the ternary FeNiMn and FeAlMn alloys. The extended mean-field renormalization group approach and a variational procedure based on Bogoliubov inequality for the free energy are employed in the pair approximation. The phase diagrams are obtained for a symmetric distribution as well as for asymmetric distributions compatible to these alloys. The obtained phase diagram for the FeNiMn system is in a much better accord with the experimental data than the previous traditional mean-field renormalization group applied to the Ising model, mainly concerning the spin-glass and antiferromagnetic phases. Better results are also achieved for the order parameter of the FeAlMn alloys.