why i dont have a admin user?

If you cannot boot into Single User Mode (not Safe Mode), you can try to run the previously posted command via Terminal in Recovery: Start up your Mac in single-user mode or verbose mode - Apple Support

Once you have mounted the startup drive in Disk Utility as directed in the above-linked article, try removing .AppleSetupDone with this command in Terminal:

rm /var/db/.applesetupdone

Restart and it should run the Setup Assistant where you can create a new Admin user.

You can then use that new user to give your old user Admin privileges.

How did you get yourself here:

Did you try to change the name on an account?

Did you delete any users?

Did you acquire this Mac from someone else (i.e. it was not purchased new)?

With regards to other things stated here:

You don't have an admin user. It may have been deleted as you would not normally have a deleted users folder.

You are not sharing with anyone. Shared is a standard folder in /Users for sharing files between users on the same Mac.

You likely do not need to turn off FileVault if the above method works.

Yes you do have it.

It does not let you unlock anything like that screen you are showing.

The lock at the bottom left.

Try to unlock it.

______

Try this

In Finder GO TO Folder type

/Users

what do you see ?

How would we know?

How to Create a New User Account if You Cannot Access Your Admin Account

Reboot the computer. At the chime press and hold down the COMMAND-S keys to start into Single-user Mode. You will boot to a black screen with scrolling white text, release the keys and wait until it finishes. Enter the following lines at the command prompt pressing RETURN after each:

    mount -uw /

               ^     ^  Note spaces

    rm /var/db/.applesetupdone

        ^    Note space

    reboot

After you reboot the computer you will be taken to the Setup Assistant. When you get to the point where you are asked to set up your new user account, create a new admin account. Be sure to name this user account something different than the admin user account that already exists on the system. When you finish the Setup Assistant, it will automatically log you into the new account.

You can transfer your files from the old account to the new one. See Transferring files from one User Account to another. Once you have moved all your files into your new account, you can delete the old account using Accounts or Users & Groups preferences.

It looks like the Admin is still logged in and it wont let you change anyhing.

Try this recovery.

To get to the point in the login process where you can reset the

password, click the question mark that appears on the right side of the

password field or just try to log in three times. After the third failed

login attempt, the Mac will prompt you with the password reminder, if

one is set, and give you the option of resetting the password using your

Apple ID.

That is not possible.

Is that a "manged" mac, from company ?

it says admin name is root,

Well you are correct, you have no other admin account beyond the root user.

I would follow Kappy directions above to setup a new admin user account. From here you can make changes and give yourself admin privileges.

From the Terminal.app copy and paste:

dscacheutil -q group -a name admin

see the output, users:

That proves there is a admin user and you are not it.

******With whom are you sharing and what access control do they have ?

Try removing that Sharing !

>>>Also Open that Deleted User folder that you see.

Right click on it and Click on Get info, then at the bottom give your self full access

A Standard user can log into his/her account with a proper password. But a Standard user cannot install or remove software, cannot access root or admin accounts, cannot access and delete system files/folders, and cannot create new user accounts.

A firmware password must be set by the owner of the hardware. Without the password no one can boot the computer, erase the OS, nor install a new OS. See How to set a firmware password on your Mac.

A firmware password differs from a FileVault password. See Use FileVault to encrypt the startup disk on your Mac. The admin user can also set a Recovery key to use if the FileVault password is forgotten: How to find your FileVault recovery key in macOS.

You might think of the Firmware password protecting the hardware while the FileVault password protects the software. Together they work to keep your computer and its content secure.

It should say more, read the last line

name: admin

password: *

gid: 80

users: root _mbsetupuser .....some name...

what is that "some name"

Choose how you want to be able to unlock your disk and reset your password, in case you ever forget your password:  

• If you're using OS X Yosemite or later, you can choose to use your iCloud account to unlock your disk and reset your password.*
• If you're using OS X Mavericks, you can choose to store a FileVault recovery key with Apple by providing the questions and answers to three security questions. Choose answers that you're sure to remember.*
• If you don't want to use iCloud FileVault recovery, you can create a local recovery key. Keep the letters and numbers of the key somewhere safe—other than on your encrypted startup disk.

Try Command V