Which solver can solve this equation for V. Result should be around 59. I tested the to halfs of the equation on python. Thank you for your directions in the first place.

(650.5-(500-V))/((150.5-V*0.5)/(V*0.8660254037844386)) = ((500-V)-((650.5/(((150.5-V*0.5)/(V*0.8660254037844386))+1.364))*1.364))/((((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/(264.77-(650.5-(500-V))/(284.7/(264.77-(284.7/((150.5-V*0.5)/(V*0.8660254037844386)))))))+1.7320508075688773))*1.7320508075688773+(500-V))-((650.5/(((150.5-V*0.5)/(V*0.8660254037844386))+1.364))*1.364))/(268.18-(((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/(264.77-(650.5-(500-V))/(284.7/(264.77-(284.7/((150.5-V*0.5)/(V*0.8660254037844386)))))))+1.7320508075688773))*1.7320508075688773+(500-V))-365.8)/(284.7/(268.18-((650.5-(500-V))/1.7320508075688773))))) monospaced

Answer 1

[Torsten]

fun = @(V)((500-V)-((650.5/(((150.5-V*0.5)/(V*0.8660254037844386))+1.364))*1.364))/((((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/(264.77-(650.5-(500-V))/(284.7/(264.77-(284.7/((150.5-V*0.5)/(V*0.8660254037844386)))))))+1.7320508075688773))*1.7320508075688773+(500-V))-((650.5/(((150.5-V*0.5)/(V*0.8660254037844386))+1.364))*1.364))/(268.18-(((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/(264.77-(650.5-(500-V))/(284.7/(264.77-(284.7/((150.5-V*0.5)/(V*0.8660254037844386)))))))+1.7320508075688773))*1.7320508075688773+(500-V))-365.8)/(284.7/(268.18-((650.5-(500-V))/1.7320508075688773)))))-(650.5-(500-V))/((150.5-V*0.5)/(V*0.8660254037844386));
format long
V = fsolve(fun,50)

Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.

V = 
  59.140215077391687

fun(V)

ans = 
    -6.500061999759055e-08

[Bruno Luong]

I would use fzero for singlle variable function

fun = @(V)((500-V)-((650.5/(((150.5-V*0.5)/(V*0.8660254037844386))+1.364))*1.364))/((((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/(264.77-(650.5-(500-V))/(284.7/(264.77-(284.7/((150.5-V*0.5)/(V*0.8660254037844386)))))))+1.7320508075688773))*1.7320508075688773+(500-V))-((650.5/(((150.5-V*0.5)/(V*0.8660254037844386))+1.364))*1.364))/(268.18-(((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/(264.77-(650.5-(500-V))/(284.7/(264.77-(284.7/((150.5-V*0.5)/(V*0.8660254037844386)))))))+1.7320508075688773))*1.7320508075688773+(500-V))-365.8)/(284.7/(268.18-((650.5-(500-V))/1.7320508075688773)))))-(650.5-(500-V))/((150.5-V*0.5)/(V*0.8660254037844386));
format long
V = fzero(fun,50)

V = 
  59.140215055311920

fun(V)

ans = 
     0

Answer 2

[John D'Errico]

So the second time you asked this question, you provided values for the other variables. I'll first put it in symbolic form so we can see what you have.

syms V
F_V = -(650.5-(500-V))/((150.5-V*0.5)/(V*0.8660254037844386)) + ((500-V)-((650.5/(((150.5-V*0.5)/(V*0.8660254037844386))+1.364))*1.364))/((((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/(264.77-(650.5-(500-V))/(284.7/(264.77-(284.7/((150.5-V*0.5)/(V*0.8660254037844386)))))))+1.7320508075688773))*1.7320508075688773+(500-V))-((650.5/(((150.5-V*0.5)/(V*0.8660254037844386))+1.364))*1.364))/(268.18-(((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/(264.77-(650.5-(500-V))/(284.7/(264.77-(284.7/((150.5-V*0.5)/(V*0.8660254037844386)))))))+1.7320508075688773))*1.7320508075688773+(500-V))-365.8)/(284.7/(268.18-((650.5-(500-V))/1.7320508075688773))))) 

F_V = 

Note that I put both onto the same side of the equation, so I can plot it, as a function of V.

fplot(F_V,[0,100])

There does appear to be a solution for this relation. As I said in my response the FIRST time you asked the question, there will be NO analytical solution. Don't even bother to look.

Just use fzero.

F_v = @(V) -(650.5-(500-V))/((150.5-V*0.5)/(V*0.8660254037844386)) + ((500-V)-((650.5/(((150.5-V*0.5)/(V*0.8660254037844386))+1.364))*1.364))/((((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/(264.77-(650.5-(500-V))/(284.7/(264.77-(284.7/((150.5-V*0.5)/(V*0.8660254037844386)))))))+1.7320508075688773))*1.7320508075688773+(500-V))-((650.5/(((150.5-V*0.5)/(V*0.8660254037844386))+1.364))*1.364))/(268.18-(((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/((((((500*2-(500-V))/3.052050807569)*1.7320508075688773+(500-V))-(500-V))/(264.77-(650.5-(500-V))/(284.7/(264.77-(284.7/((150.5-V*0.5)/(V*0.8660254037844386)))))))+1.7320508075688773))*1.7320508075688773+(500-V))-365.8)/(284.7/(268.18-((650.5-(500-V))/1.7320508075688773)))));
[Vsol,fval,exitflag] = fzero(F_v,[0,100])

Vsol = 59.1402

fval = 0

exitflag = 1