If they're paid and show a good history of on-time payments, it's fine that they're there. But, if you only got an Equifax report, you've only got about 1/3 the story. There are two other companies that report credit history as well, Transunion and Experian.
I have successfully cleaned up my credit, on my own, without paying a dime for anyone else to do it (other than a small cost for all three reports in a preferred format).
1> Get all three credit reports. I recommend going to www.freecreditreport.com and signing up to get all three from them (Equifax). It's $25, but that is a small price to pay for a good service. You get all three in one report, side by side, so that you see what information each account you have is held by each credit reporting company very easily. Watch out though. Equifax's "free" credit report signs you up for credit monitoring. If you want that, great. If not, you'll have to cancel that once you have all three reports. There are other companies out there that will give you all three as well. Shop around. The important part is to get all three! (If you decide to go the totally free route, that is fine too.)
2> Accounts will stay on your credit report 7 years from the data of the last activity on that account. What that means is, hypothetically, you have a credit card and decide to stop paying on it... the clock starts from the last payment you've made. Seven years from that date, charged off account or not, it comes off your credit reports, all three of them. If, two years into it, you decide to try to make a payment... Ooops! Guess what? You just started the clock over. What I've found is that very close to that seven year mark, you will start to receive all these offers in the mail from collection agencies, or others, offering to settle the account for a significant amount les that the full amount owed. This is a trick. They know the account is about to become uncollectable. Tear those offers up and wait.
3> Now, say you have all three reports and you notice strange items, or strange information. What you do is you write up a letter of dispute and send it to each credit reporting company who has the incorrect information. You cannot legally dispute items that are legitimate. Very important, that.
Now, the credit reporting companies are required by law to forward the dispute on to the owners of the accounts on your credit report that you are disputing. They have 30 days to respond. If they do not respond in 30 days, guess what? They have to take it off your credit reports immediately.
I just did a quick web search and came up with this site that has what looks like are some good dispute letter templates - https://www.eloan.com/s/show/cr-contact
I will be more than willing to answer any questions you have. I'm no pro, and take no responsibility for what you do with this info, but I've at least been through the process. (My ex-wife managed to get a car taken off her credit this way! )