How to evaluate a unknown variable?

I am trying to evaluate a specific variable, i.e., lambda from the following expression:

alpha=0.9;
g=[3, 2, 1];
N=10;
P=5;

sum(( lambda*(2-alpha)-sqrt(lambda*alpha*(lambda*alpha+g.*4*(1-alpha))) ) ./ ( g.*2*lambda*(alpha-1) )) = N*P

Which function shall I use to find the value of lambda that satisfies the equality above, since it is the only unknown variable?

[Guillaume]

You could use fzero if your equation made sense. On the left side of your equation you have a 3 element vector (with 3 different values obviously). On the right hand side you have a scalar.

Answer 1

[Peter Jarosi]

Using fsolve:

alpha=0.9;
g=[3, 2, 1];
N=10;
P=5;
f = @(lambda) sum(( lambda*(2-alpha)-sqrt(lambda*alpha*(lambda*alpha+g.*4*(1-alpha))) ) ...
    ./ ( g.*2*lambda*(alpha-1) )) - N*P;
lambda0 = 1;
options = optimoptions('fsolve','Display','iter','Algorithm','levenberg-marquardt');
lambda = fsolve(f, lambda0, options);

Learn more at https://www.mathworks.com/help/optim/ug/fsolve.html

[Miroslav Mitev]

That works, thank you :)

[Peter Jarosi]

You're very welcome! :)