  We express the solutions to quadratic equations with two variables in the
ring of integers using EDT0L languages. We use this to show that EDT0L
languages can be used to describe the solutions to one-variable equations in
the Heisenberg group. This is done by reducing the question of solving a
one-variable equation in the Heisenberg group to solving an equation in the
ring of integers, exploiting the strong link between the ring of integers and
nilpotent groups.
