how to solve the non-linear equation

I tried many times. I couldn’t get the answer for the below equation. Kindly let me help to solve the equation.

D=1050;c=25; A=1000; B=1000;v=1.077; γ =0.1; β =0.1; 
V*c*(1-γ)*Q^3+v*c*A*Q^2-2*c*A*Q+v*c*(1- γ)*B*D*Q^(1- β)+v*A*B*D*Q^(-β)=0

[Ameer Hamza]

First, Matlab variable name only allows alphanumeric characters. $\gamma$ and $beta$ are not allowed. Second, what is the variable for which you want to solve this equation?

Answer 1

[Stephan]

To solve for V as a function of Q:

syms V Q
D=1050;
c=25; 
A=1000;
B=1000;
v=1.077;
gamma =0.1;
beta =0.1; 
eq = V*c*(1-gamma)*Q^3+v*c*A*Q^2-2*c*A*Q+v*c*(1- gamma)*B*D*Q^(1- beta)+v*A*B*D*Q^(-beta)==0;
sol_V = isolate(eq,V);
pretty(sol_V)

gives:

       /                                                     9/10 \
       |        2             1130850000   6830105296895999 Q     |
       | 26925 Q  - 50000 Q + ---------- + ---------------------- | 2
       |                          1/10            268435456       |
       \                         Q                                /
V == - --------------------------------------------------------------
                                        3
                                    45 Q