  We generalize the known solution of the Schr\"odinger equation, describing a
particle confined to a triangular area, for a triangular graphene quantum dot
with armchair-type boundaries. The quantization conditions, wave functions, and
the eigenenergies are determined analytically. As an application, we calculate
the corrections to the quantum dot's energy levels due to distortions of the
carbon-carbon bonds at the edges of the quantum dot.
