In 2019 the LHCb experiment discovered for the first time a clear signal of direct CP violation in the charm sector, in particular in the decays of D0 mesons to π+π− and K+K−. However, the theoretical determination of the strong part of the related decay amplitudes in the SM remains uncertain, mainly due to the difficulties when dealing with charmed hadronic asymptotic states. A long-known tool for assessing such amplitudes is dispersion relations. These arise from fundamental properties of the S-matrix elements and are data driven at large . Although they are easily understood and deployed in elastic channels, they become much more complicated when inelasticities are present. In this work we extract the CP-even and odd D→ππ/KK amplitudes within the SM, analysed in the isospin basis and with the use of unitarity and large number-of-colours expansion, by performing global fits to the current experimental data. Moreover, we implement novel numerical methods for dispersion relations in the inelastic isospin-0 channels.