Cubic equations with independent variables

[omarxx84]

Hi colleages. can you help me to solve the cubic equation below:
2N(Ep-En)hp^3(x)-3[M(x,t)(Ep-En)-2NEnh]hp^2(x)-6Enh[M(x,t)+Nh]hp(x)+Enh^2[3M(x,t)+2Nh]=0 notice that all variables in the equation are dependent on x only, except M is dependent on x and t.
En, Ep, N and h are constants.
i know the solution when the equation dependent on one variable, but the problem is that M dependent on two variables x and t.
please help me and i will be very grateful for you...

 

[Mark44]

Please don't double post! (Or triple post!) This is the third thread that you have started with exactly the same problem: https://www.physicsforums.com/showthread.php?t=407426 and https://www.physicsforums.com/showthread.php?t=403107.

In one of the other threads someone asked you to rewrite the equation in a less dense form. With everything so tightly packed together, the equation is difficult to comprehend.

 

[omarxx84]

i am so sorry,

 

[Mark44]

There is an algorithm for finding the roots of a cubic equation - see http://en.wikipedia.org/wiki/Cubic_equation. Using this algorithm might help you solve for the values of p(x) that are roots of your equation.

You haven't said anything about p(x). What information do you have about this function?