Cubic equations with independent variables

AI Thread Summary
The discussion revolves around solving a complex cubic equation where most variables depend solely on x, while M depends on both x and t. The original poster seeks assistance due to the added complexity of M's dependence on two variables, which complicates finding solutions. Other participants suggest using a cubic equation root-finding algorithm and recommend rewriting the equation for clarity. There is a request for more information about the function p(x) to aid in solving the equation. Overall, the thread highlights the challenges posed by the equation's structure and the need for clearer presentation and additional context.
omarxx84
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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...
 
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i am so sorry,
 
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?
 

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