Greek and Latin letters in verbatim

Set the font encoding to T1 inside verbatim:

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[greek]{babel}
\usepackage{alphabeta}

\makeatletter
\renewcommand\verbatim@font{\normalfont\fontencoding{T1}\ttfamily}
\makeatother

\begin{document}

\begin{verbatim}
για κάθε t:
    x1 = x0 + u*Δt
\end{verbatim}

\end{document}

My problem was fixed after refactoring the \usepackage command:

\usepackage[english, greek]{babel}

and inserting the command

\selectlanguage{english} before the verbatim