We study a type Ia supernova explosion using three-dimensional numerical simulations based on reactive fluid dynamics. We consider a delayed-detonation model that assumes a deflagration-to-detonation transition. In contrast with the pure deflagration model, the delayed-detonation model releases enough energy to account for a healthy explosion, and does not leave carbon, oxygen, and intermediate-mass elements in central parts of a white dwarf. This removes the key disagreement between simulations and observations, and makes a delayed detonation the mostly likely mechanism for type Ia supernovae.