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Solve large equation with parameters?

Posted 3 years ago
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I have a very large expression:

j - Sqrt[q^2 + qp^2 - 
   2 q qp Cos[\[Theta]]] - \[Sqrt](qp^2 + 
     1/2 (16 m5^2 + ma^2 + mp^2 - 
        Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 - 
         4 (ma^2 mp^2 - 16 m5^2 qp^2)])) == 0

where

\[Theta] = Pi/6; ma = 980; mp = 139;
 j = \[Sqrt](q^2 + 
    1/2 (16 m5^2 + ma^2 + mp^2 + 
       Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 - 
        4 (ma^2 mp^2 - 16 m5^2 q^2)])) 

And $qp$ is real and positive. I want to find qp as function $q>0$ and $m5>0$ (if it is imposible then function only $q>0$ and $m5=constant=100>0$). I atemted to solve this the next way:

Solve[ j - Sqrt[
     q^2 + qp^2 - 
      2 q qp Cos[\[Theta]]] - \[Sqrt](qp^2 + 
        1/2 (16 m5^2 + ma^2 + mp^2 - 
           Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 - 
            4 (ma^2 mp^2 - 16 m5^2 qp^2)])) == 0 && qp > 0 , qp, 
  Reals];

Mathematica hangs after two hour calculation. Where I am wrong? After calculation I want to plot function form: $z=q^2+m5^2$ (in reality this is more complicated)

x-post on MSE: link

Please add links to/from x-post on MSE.

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