Using maple I am trying to solve for q from this big linear equation.

\begin{equation}

\frac{\gamma*q*P_Q}{k_p*(1-q)*P_C} = \frac{I*\alpha}{k_f+k_d+\frac{k_n*\lambda_b*\gamma *q*P_Q}{\lambda_b*\gamma*q*P_Q+k_p*\lambda_r*(1-q)^2}+k_p*(1-q)}

\end{equation}

Values of parameters are given below:

$I=1200$

$k_f = 6.7*10.^7$

$k_d = 6.03*10.^8$

$k_n = 2.92*10.^9$

$k_p = 4.94*10.^9$

$\alpha = 1.14437*10.^(-3)$

$\lambda_b = 0.87e-2$

$\lambda_r = 835$

$\gamma = 2.74$

$P_C = 3*10.^11$

$P_Q = 2.87*10.^10$

=>

I tried in maple does not work.

Code:

k_f = 6.7*10.^7;
I=1200;
k_d = 6.03*10.^8;
k_n = 2.92*10.^9;
k_p = 4.94*10.^9;
alpha = 1.14437*10.^(-3);
lambda_b = 0.87e-2;
lambda_r = 835;
gamma = 2.74;
P_C = 3*10.^11;
P_Q = 2.87*10.^10;
(gamma*q*P_Q)/(k_p*(1-q)*P_C) = I*alpha/(k_f+k_d+k_n*lambda_b*gamma*q*P_Q/(lambda_b*gamma*q*P_Q+k_p*lambda_r*(1-q)^2)+k_p*(1-q));

I even tried in Matlab with fzero function solver, still does not works.