How to run /sbin/fsck -fy on the recovery partition if filesystem is unknown
I take no responsibility for what happens to your mac. The command line can destroy your working computer. Fsk can fix things better than disk utility though.
If you agree, open terminal on your the mac.

To repair disks first find their disk identifiers. They are all different.
In the terminal type without quotes "diskutil list"

In the left-hand column, you will see all identifiers for the drives unmounted and mounted. it will look like this disk2b1, put this in the the diskabc position below.

In the "sudo /sbin/fsck -fy /dev/diskABC"

Type your password for best effect! You will not see the characters of the password so type well.