You can try the formula below by Shirley Scott or you can go to Obituary Central's Birthday Calculator to figure out the date.
You need to find the date of birth of your ancestor. The tombstone says they died at 71y, 7m, 9d on May 6, 1889. Follow these simple instructions for an accurate way to find their date of birth.
Using a calculator, enter date of death in numbers by year, month and then day.
1889 May 6 would be entered as 18890506.
Subtract the age of person found on a tombstone. 71 y, 7 m, 9 d would be entered as 710709. Subtract that from 18890506. You will get an answer of 18179797.
Subtract 8870 from 18179797 to correct the months and days. The answer will be 18170927.
Translate 18170927 back into year, month and day. You will have 1817 September 27 as the date of birth.