The value of this quarter is a quarter. The mint made millions and millions of these and they were and are collected by many people, which means that the coin is not rare or unique, unless there is some error. If you found the coin in general circulation, again, it is worth 25 cents. Even this particular coin in BU UNC condition would not command any premium due to the sheer number of coins that are available.
All state quarters were minted in huge numbers so any you find in change are only worth face value.
There are a couple of errors among the state quarters (Delaware with a rotated reverse, Iowa with an extra leaf) but none among the North Carolina set.
25 cents. Remember, 1789 isn't the year the coin was minted - that date is by the bottom rim - it's the year North Carolina was admitted to the Union.
First Flight
North Carolina
"North Carolina became the 12th state on November 21, 1789. Governor James B. Hunt had several state groups and coin collectors evaluate design ideas from the people of North Carolina. The governor and his committees selected the "First Flight" design idea to represent their state quarter. The words "First Flight" are in the center of the quarter." - Excerpt from page linked below. It is a shame that people who designed the quarter didn't see how misleading it is to place the year 1789 above "First Flight". In fact the Wright brothers had their first flight at Kitty Hawk, North Carolina on December 17, 1903.
North Carolina
Orville and Wilbur Wright at Kittyhawk North Carolina.
North Carolina is credited with the first flight. It is also the logo on their license plates
in kitty hawk North Carolina
Kitty Hawk North Carolina
The first flight of the Wright flyer took off from Kitty Hawk North Carolina, and landed 120 feet away in Kitty Hawk North Carolina.
The Wright brothers' first flight was at Kill Devil Hill, Kittyhawk, North Carolina.
The Wright Brothers made their first flight in Kitty Hawk, North Carolina.
The first successful flight of their glider was Kitty Hawk, North Carolina.