# How can I calculate the value in an equation?

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Ali Deniz on 26 Apr 2022
Edited: Sam Chak on 27 Apr 2022
gamma=1.4
V_M_2 = 20;
V_M_2 = sqrt((gamma+1)/(gamma-1)) * atan(sqrt((gamma-1)/(gamma+1)*(M_2^2-1)))-atan(sqrt(M_2^2-1))
How can I find the M_2 from this equation? Thank you.

Sam Chak on 26 Apr 2022
Please verify if the nonlinear equation is correct. Looks like there are no real solutions for this one.
Sam Chak on 27 Apr 2022
Edited: Sam Chak on 27 Apr 2022
@Ali Deniz, Thanks for the correction. By the way, the nonlinear function has a limit, .
So, if , then it has roots. Please check again.
gamma = 1.4;
V_M_2 = 2.0;
% function to be solved
f = @(x) sqrt((gamma + 1)/(gamma - 1))*atan(sqrt((gamma - 1)/(gamma + 1)*(x^2 - 1))) - atan(sqrt(x^2 - 1)) - V_M_2;
% initial guess
x0 = 20;
% root-finding solver
xsol = fzero(f, x0)
xsol =
17.9584 ### More Answers (1)

Torsten on 26 Apr 2022
I don't see a root:
gamma=1.4
V_M_2 = 20;
fun = @(M_2)V_M_2 - (sqrt((gamma+1)/(gamma-1)) * atan(sqrt((gamma-1)/(gamma+1)*(M_2-1)))-atan(sqrt(M_2-1)));
M_2 = -20:0.1:200;
plot(M_2,fun(M_2))