solve equation for a variable

I'm sure this sort of thing has been posted numerous times, but I can't find anything that works for me for whatever reason. I need to solve an equation for a variable, and I can't remember how to do this. It's been a while since I've used matlab. I need to solve for t numerically. This is the last thing I tried:

v = 2.42;

si_f235 = 577E-24;

N_235 = 780.63E18;

phi = 3E13;

si_a235 = 101E-24;

si_a238 = 2.73E-24;

N_238 = 21.52E21;

n = 1.5;

eqn = @(x) v*si_f235*N_235(1-si_f235*phi*x)/(si_a235*N_235*(1-si_a235*phi*x)+si_a238*N_238*(1-si_a238*phi*x))==n;

t = vpasolve(eqn , x)

it's just telling me that x is an unrecognized variable

Answer 1

[Anton Kogios]

This works for me (you were also missing an * in your equation):

v = 2.42;
si_f235 = 577E-24;
N_235 = 780.63E18;
phi = 3E13;
si_a235 = 101E-24;
si_a238 = 2.73E-24;
N_238 = 21.52E21;
n = 1.5;
syms x
eqn = v*si_f235*N_235*(1-si_f235*phi*x)/(si_a235*N_235*(1-si_a235*phi*x)+si_a238*N_238*(1-si_a238*phi*x))==n;
t = vpasolve(eqn , x)

t = 

47756908.067411697270732667471209

[SETH SCHREINER]

it's giving me an error for syms x now

[SETH SCHREINER]

oh i dont have the right toolbox apparently

[Anton Kogios]

Yes sorry, this requires the Symbolic Math Toolbox, which is very helpful for these sorts of problems. You could of course always follow Torsten's advice in his answer.

Answer 2

[Torsten]

You don't need a toolbox for this.

Take a piece of paper and a pencil, multiply the equation by the denominator of the left-hand side, collect terms with x on one side and other terms on the other side, factor out x on the one side and solve for x.

It's just like solving 3*x + 5 = 7*x - 4 for x.

[SETH SCHREINER]

I get how to do it on pencil and paper, but the equation gets rather tedious trying to separate out x from the other variables towards the end