Same way you would do it in lisp - you'd build a function to do pattern matching and use conditionals to test which pattern is matched.

    (defun solve-poly (p)
        (if (match '(+ (* ?a x) ?b) poly))
            (-b/a  where b, a come from (extract-values-from-pattern-match poly))
           (some code for second order)
     ))

(Some code borrowed from lispm's comment. Not sure which library the match function comes from.)