Page conditional on form submit

I want to direct a user to one front-end page if their front-end form submission meets certain criteria, and to a different front-edn page if the submission doesn’t meet the criteria. Something along the lines of:

if($submit == 'incorrect response') {
    // go to incorrect_page_slug
} else {
    // go to correct_page_slug
}

On the backend (Admin), I would simply use wp_redirect, but this function does not work on the front end.

My site is currently being developed on a local server, so I cannot post a link.

Also, please do not respond with “use such-and-such plugin” to do this. I have spent 3 months testing every form-handling plugin I could find here, and none of them can do many-to-one database updates very fluidly, or at all.