How to display search results in admin theme?
At the code level you can use hook_admin_paths(), e.g.

function MYMODULE_admin_paths() {
  return array(
    'search/*',
  );
}


Or if you'd rather use a non-code solution, you could install a module like ThemeKey


  ThemeKey allows you to define simple or sophisticated theme-switching rules which allow automatic selection of a theme depending on current path, taxonomy terms, language, node-type, and many, many other properties.