When you lost your root password in a RedHat Linux Based systems you should first have access to the console, (the machine itself).
Power on, or reboot as needed.
and as soon as you get this screen (or similar depending your system and configurations)
Now you should press 'e' and you will get this screen.
Select the image you would like to boot, and press 'e' again, and as soon as you get the next screen
Insert an space and the number one '1' as shown in the image.
Your will now have your System booted as a single user and you will have no need to enter a password.
Now you can change the password like this
And you will have again your system working.
Here you can see the last two images, showing this.