Criteria for Solving this equation

[smooney]

Is it possible to solve this equation in terms of H without knowing any numbers? If so what method would I use? If I had numbers I think I could solve it numerically in excel. It's been a few years since I was in school and am fairly (very) rusty:

H^5 -10*L*H^4 +25*L^2*H^3 -25*Q^2/K^2 = 0

L,K = Constant

Any help would be appreciated, Thanks!

 

[SteamKing]

You have a fifth order polynomial in H. There is no general formula which can solve this equation. If you have numerical values for your constants, then an iterative procedure (perhaps using Excel) would be the way to calculate solutions.

 

[JJacquelin]

There is no simple formula giving Y as a function of L, H, Q, K because it is a polynomial equation of the fifth degree.
Such formula exists, but involving special functions : the Jacobi theta functions. But, in practice, it is much simpler to use numerical methods to solve the equation.