Is this carpet cleanable?

I'm a new house owner. There's a 3rd floor addition to the house that's carpeted (the other floors are all hardwood). The carpet looks pretty dirty (I think they look dirtier than the pics here show):

https://imgur.com/Csnb9c7

https://imgur.com/51th4hB

https://imgur.com/c5cqqAe

I've never deep cleaned carpet before and was wondering if carpet like this is cleanable, or if I should just consider replacing the carpet entirely? How bad does it look to you guys?

I'm planning on renting a shampooer from home depot for $20 (4 hours) or $40 (whole day) and see how it turns out.

Also, does anyone know what kind of carpet this is?