  We prove effective equidistribution theorems, with polynomial error rate, for
orbits of the unipotent subgroups of $\operatorname{SL}_2(\mathbb R)$ in
arithmetic quotients of $\operatorname{SL}_2(\mathbb C)$ and
$\operatorname{SL}_2(\mathbb R)\times\operatorname{SL}_2(\mathbb R)$. The proof
is based on the use of a Margulis function, tools from incidence geometry, and
the spectral gap of the ambient space.
