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Using the MAMI-C microtron at an accelerator facility in Mainz, Germany, fixed target experiments carry on to study the excitation spectrum of the nucleon via the photoproduction of mesons. In this paper, the photon-induced production of the π0π+/- -pairs with a liquid deuterium target has been investigated in view of the helicity dependence of the two isospin channels. While unpolarized cross-sections for protons and neutrons have been extracted, this data alone is not sufficient to separate the resonances, therefore polarization observables are vital factors essential in disentangling the contributing resonant and non-resonant amplitudes. The double-polarization observable E was extracted with the help of a longitudinally polarized deuterated butanol target and a circularly polarized photon beam. The antiparallel and parallel spin configurations between the beam photon and the target nucleon imply the spin-dependent cross-sections σ1/2 and σ3/2, respectively, which have been derived from E. Reaction products were detected with an almost 4π solid-angle covering calorimeter composed of the Crystal Ball, TAPS detectors, and particle identification detectors. The results are sensitive to sequential decays of nucleon resonances that include intermediate states and also involve the emission of charged ρ mesons. Furthermore, comparative studies of the results of the most recent available model calculations were made. [ABSTRACT FROM AUTHOR]