Un-able to interpret math results

Questions
,
1

Really not sure what some of these symbols

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Capture.PNG680×458 60.9 KB

mean. Any help interpreting this would be great.

2

They are parametrized roots to a polynomial equation of degree 6.

3

Thank you for your response. I am not sure what that means. I am looking for a function F(D), K & R are constants.

4

You have six such solutions, each a parametrized branch of polynomial roots.

In Mathematica:

solns = ff /. Solve[dd == ff/kk + z*(ff/rr)^6, ff]

(* Out[73]= {Root[dd - #1/kk - (z #1^6)/rr^6 &, 1], 
 Root[dd - #1/kk - (z #1^6)/rr^6 &, 2], 
 Root[dd - #1/kk - (z #1^6)/rr^6 &, 3], 
 Root[dd - #1/kk - (z #1^6)/rr^6 &, 4], 
 Root[dd - #1/kk - (z #1^6)/rr^6 &, 5], 
 Root[dd - #1/kk - (z #1^6)/rr^6 &, 6]} *)

One can give the parameters actual numeric values in order to get numeric solutions. For example:

solns /. {dd -> 3.3, kk -> 5.2, rr -> 1.07, z -> 2.8}

(* Out[74]= {-1.11127, 1.08777, -0.544166 - 0.962542 I, -0.544166 + 
  0.962542 I, 0.555916 - 0.942204 I, 0.555916 + 0.942204 I} *)