I tried this:

tan(2*(1.1575*10^12/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2))/tan(2*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2)) = -4*x^2*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*(1.1575*10^12/(1-.5)^1.2-x^2)^(1/2)/(1.1575*10^12/(1-.5)^1.2-2*x^2)^2;

lhs(%)-rhs(%);

RootOf(%, x);

z0 := allvalues(%);

evalf(%);

i get 6 solutions but they seem incorrect:

-1.127205209*10^6, -1.129691937*10^6, -9.942135523*10^5, -1.630716619*10^6, -1.630716619*10^6, 1.129691937*10^6

one of the solutions should be 1.131417176*10^6 (i know this is definately a solution)

I typed in maple:

tan((1/500000)*(a-z)^(1/2))/tan((1/500000)*(b*a-z)^(1/2))+4*z*(b*a-z)^(1/2)*(a-z)^(1/2)/(a-2*z)^2; RootOf(%, z); allvalues(%)

value a is outputted. What is this value? why am i not seeing a number?

I typed in maple:

tan((1/500000)*(a-z)^(1/2))/tan((1/500000)*(b*a-z)^(1/2))+4*z*(b*a-z)^(1/2)*(a-z)^(1/2)/(a-2*z)^2; RootOf(%, z); allvalues(%)

value a is outputted. What is this value? why am i not seeing a number?

yes your above equation looks correct, what solutions do you get when you do 

               1/2
                (a - z)
            tan(----------)                 1/2        1/2
                  500000       4 z (b a - z)    (a - z)
           ----------------- + ---------------------------     =     0   ?
                        1/2                     2
               (b a - z)               (a - 2 z)
           tan(------------)
                  500000

yes your above equation looks correct, what solutions do you get when you do 

               1/2
                (a - z)
            tan(----------)                 1/2        1/2
                  500000       4 z (b a - z)    (a - z)
           ----------------- + ---------------------------     =     0   ?
                        1/2                     2
               (b a - z)               (a - 2 z)
           tan(------------)
                  500000

Also can you tell me how i can systematically obtain these solutions, rather than searching for them using intervals (with fsolve function).

Basically how can I solve and display all of the solutions at once?

Also can you tell me how i can systematically obtain these solutions, rather than searching for them using intervals (with fsolve function).

Basically how can I solve and display all of the solutions at once?

Axel Vogt

I get solution 

1.131417176*10^6 for that equation.

Can you please check for the equation:

tan(4*(1.1575*10^12/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2))/tan(4*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2)) = -4*x^2*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*(1.1575*10^12/(1-.5)^1.2-x^2)^(1/2)/(1.1575*10^12/(1-.5)^1.2-2*x^2)^2

that you get solutions:

I have put in bold, what has changed from your orevious equation.

Axel Vogt

I get solution 

1.131417176*10^6 for that equation.

Can you please check for the equation:

tan(4*(1.1575*10^12/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2))/tan(4*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2)) = -4*x^2*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*(1.1575*10^12/(1-.5)^1.2-x^2)^(1/2)/(1.1575*10^12/(1-.5)^1.2-2*x^2)^2

that you get solutions:

I have put in bold, what has changed from your orevious equation.

tan(2*(1.1575*10^12/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2))/tan(2*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2)) = -4*x^2*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*(1.1575*10^12/(1-.5)^1.2-x^2)^(1/2)/(1.1575*10^12/(1-.5)^1.2-2*x^2)^2

How do you post as text?