Simple algebraic equations take too long to solve

I have been trying to solve these following equations to calculate the value of u and v. but it is taking forever to solve. Kindly look into this.

Thank you

trail.nb (10.7 KB)

In your case is Sextic equation ,Solve give you solution by Root function.I used Eliminate, because Solve hangs up.

Equation ver2.nb (4.39 MB)
Untitled _OP_2_CP_.pdf (2.38 MB)

Thank you for replying. that’s really helpful

Hii Mariusz… how long did it take so solve this. In my case its been more than 8 hours and it is still running.

A 1 hour computation then I Aborted.

I have simplified version see attached file.

Equation ver3.nb (136 KB)

Thankyou for your kind reply. That’s really helpful

Hi
Thanks everybody to take part into this discussion, I am also facing the same problem. Solve command taking too much time. Couple of times, mathematica kernel also quite.
How to avoid this problem

You replaced N -> n, but n was already a parameter.