4=5?

Today,my lecturer's question,how could be 4=5?
base on normal mathematical method to solve this question,4=4 finally,u will get 4=5.
oh.i was suprised about it. this subject is called real analysis.i'd reseat this subject now.Base on my mathematical knowledge,i felt that i can't use normal logical thinking to solve it anymore.At this moment, i know what is called knowledge is power.you can create some theory that people believe u, then u will be success.no matter that is right or wrong.Most of the time, you can't even differenciate it is right or wrong.
when i m keep growing up,i felt there is No equality in this world. i have to accept.4=5.otherwise,u find out the mistake and theoreom to prove it is wrong.the question i've shown below.if anyone know exactly the answer please let me know.thanks.



4(-5) = 4(-5)
16-36 = 25-45
4² - 9(4) = 5² - 9(5)
4² - 9(4)+ 81/4 = 5² - 9(5)+ 81/4
(4 - 9/2)² = (5 - 9/2)² (completing aquare)
√ (4 - 9/2)² =√ (5 - 9/2)² (square root both side)
4 - 9/2 = 5 - 9/2
4=5 ?????