re allocate the Boot recovery partition space to the main system I am very new to apple, 
I tried look up answer but was afraid to mess thing up more and loose data so decided to ask for precise answer here.

I have hard drive on my mac of 750GB, and decided to divide it to 2 partitions, 450 and 300 but then I deleted the 300G but these 300 GB now have been added to the Apple Boot recovery HD and I can't use it. 

I will attach a photo through the terminal.
Please let me know how can I reuse that space and add it to the main system hard drive.
I'd make a backup of your system and then format the partition altogether.

You cant merge the boot recovery with the Mac partition. It's separate so that you can troubleshoot the mac if you need to reinstall it which is what I recommend.

As for resizing the MacOS boot partition to a smaller size, you can try this fix from this question: https://superuser.com/a/985499/841637


  To fix:
  
  
  Boot into the OS as normal.
  Open a terminal.
  Repair the disk diskutil repairVolume /dev/disk0s3 (where disk0s3 is your volume)
  Verify the disk diskutil verifyVolume /dev/disk0s3
  Resize the partition diskutil resizeVolume /dev/disk0s3 650M
  Boot into the recovery mode
  Open the terminal, don't use the Disk Utility
  Resize the actual disk diskutil resizeVolume /dev/disk0s2 200G (where disk0s2 is the actual disk you want to resize, 200G is your
  size)
  


Just make sure that your drive volume names are in place of the volumes inserted in the list above.

See if you are able to do this.