The spin-glass Blume-Capel model is studied by using an extended mean-field renormalization group approximation. The effects of a probability distribution of the bilinear interaction coupling with competing interactions have been investigated. The phase diagrams show second-order phase boundaries among ferromagnetic, antiferromagnetic, paramagnetic, and spin-glass phases. On the other hand, tricritical phenomena exist only for certain values of the concentration of ferromagnetic bonds as well as ratios of the ferromagnetic to the antiferromagnetic competitive interactions. An application to the magnetic properties of ternary system Fe-Al-Mn alloys is presented. Good fittings to the experimental data are obtained.