how can I solve this equation? I am trying with 'solve' function but getting error [ empty sym ]

2.82167 - 0.0092752*(T_f - 216.65)*(5.94429e-11*(0.387*(4.12514e8*T_f - 8.93711e10)^(1/6) + 0.6)^6 - 0.0123334)^(1/3) - 4.94073e-10*T_f^4

Answer 1

[Azzi Abdelmalek]

eq='2.82167 - 0.0092752*(T_f - 216.65)*(5.94429e-11*(0.387*(4.12514e8*T_f - 8.93711e10)^(1/6) + 0.6)^6 - 0.0123334)^(1/3) - 4.94073e-10*T_f^4'
sols=solve(eq)

[omkar bichkar]

I have tried with this but getting error

Answer 2

[Walter Roberson]

The equation has two solutions that are complex conjugates of each other. The solutions involve the roots of a polynomial of degree 72. When you use solve() you might be able to get back the unevaluated RootOf() describing the solution, but if it works it is likely to take a fair bit of time. You would then need to double() or vpa() the RootOf() to get an understandable value.

You would probably be better off just going for vpasolve() immediately. Do not be surprised if it only returns one value; just apply conj() to get the other one.

[3.4419806596342+299.9226759785752*i, 3.4419806596342-299.9226759785752*i]

[Walter Roberson]

To clarify:

syms T_f
sols = vpasolve(2.82167 - 0.0092752*(T_f - 216.65)*(5.94429e-11*(0.387*(4.12514e8*T_f - 8.93711e10)^(1/6) + 0.6)^6 - 0.0123334)^(1/3) - 4.94073e-10*T_f^4, T_f);

If you do not have the symbolic toolbox then other approaches will need to be used.