I need help with increasing the size of the file-system partition. Partitioning-o-phobia!

When I firstly installed Ubuntu I gave it 20GB of space for the filesystem. ...time passed and I get a message "the system has only 300MB available" so I need to enlarge the filesystem.

Here's my partition table:

I'm a total noob to partitioning and I have a horrible experience with it; once i had this problem: https://askubuntu.com/questions/383551/fix-partition-or-rescue-data-from-it-i-used-ddrescue on my notebook. Thanks to the great support I got, I gained the tumbleweed badge and I couldn't fix it and I had to re-install windows. The notebook didn't have much important data but this computer's much more important to me. I have backed up the data on the "Database" partition.

anyways

I need step-by-step instructions how to take space from the "Database" partition to enlarge my "filesystem" partition. and what about that red exclamation mark at /dev/sda6? how do I deal with it? ... what is it?? The red exclamation is not gone!

Tell me any extra information you need to know. Thanks in advance! :D

From the comments op said that he wants 50 GB space from the /dev/sda6 partition and add that space to the /dev/sda7 root partition.

• In the gparted screenshot,it was clearly shown that there was an exclamatory mark for dev/sda6 ntfs partition which means windows was not fully shutdown.You have to remove the exclamatory mark to resize that ntfs partition.




• To remove the exclamatory mark,boot into Windows,insert the ubuntu live disk then restart your pc(not shutdown).




• On the startup press function+Fx key to enter into the bios.




• Now change the boot-order to ubuntu live disk as first option and save the changes.




• It will boot from the live-disk,now open gparted.




• Now the remark for the ntfs partition will be gone.Make sure that no partitions
  from the /dev/sda disk would be mounted.




• Right-click on the dev/sda6 and click on Resize/Move option to shrink the space and get out of 50 GB space from that partition.




• An unallocated space of 50 GB was created just below to the /dev/sda6 partition.Now you have to move the unallocated space to just below to the /dev/sda7 partition so that the size of /dev/sda7 partition will be increased.





• Right-click on the /dev/sda6 partition and then select Resize/Move option.Now drag the slider to the extreme right so that the unallocated space move above to the sda6 Database partition.




• Next right-click on the /dev/sda5,and follow above step to move the unallocated space just above to the /dev/sda5 partition.Same operation would be done on the linux-swap partition.




• Now the unallocated space was just above to the linux-swap and just below to the dev/sda7 root partition.




• Now right-click on the dev/sda7 partition to increase it's space.That's all.I hope it would be helpful.