Welcome and thanks for your question!
Sorry to hear about your financial situation. You are right in that paying the minimum payment will probably take a long time to pay off. You have a few options to try and get your debt paid down more quickly.
1) Pay the amount listed on your credit card statement in order to pay the debt down in three years. Typically these amounts are only a few dollars more than the monthly minimum payment.
2) Start to pay your debt down using the "snowball" method. Under this method, you make the minimum payments on all your cards except the one with smallest balance. Pay whatever extra you can afford to the smallest balance. When that is paid off, move on to the next card and so and so forth. A useful calculator can be downloaded at this link
and allows you to play around with different scenarios to see how fast your debt can be paid off.
3) Try and call your credit cards and see if they will lower your interest rates. Since less will be going to interest every month, you'll be able to pay off your debt quicker. I would do this regardless if you go with option 1 or 2. Not all cards may lower your rates, but it never hurts to ask.
4) You can attempt to negotiate settlements with your credit card holders, but be aware that in many cases, they will not negotiate with you if your account is good standing and typically look for paydowns in under six months.
I wouldn't recommend working with any of the companies that advertise themselves as debt consolidation or debt settlement companies. Your payments may be reduced if you sign up with them, but usually these companies collect their fees upfront and then attempt to negotiate payments with the credit cards later, at the expense of your own credit scores.
I recommend that whatever option you decide that you have a solid plan. Make a budget for yourself detailing out all your expenses. See if there is anything you can cut and then throw that towards debt. The more determined you are, the quicker you can probably do it.
Please let me know if you have any follow-up questions or need any clarification and I will gladly assist you. If not, then please rate this answer with a positive rating. Have a wonderful evening!