Solve x in Unsolvable Equation: d/(1-COS(L/(2*x)))

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SUMMARY

The equation x = d/(1-COS(L/(2*x))) with parameters L = 28 and d = 0.2 is unsolvable by algebraic methods. Users have reported achieving approximate solutions through numerical techniques. A numerical solution using Maple yields x ≈ 1.0618829, while a trial-and-error method resulted in an approximate value of x ~ 490. Tools like TI-89 and Mathematica are ineffective for this specific equation.

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Solve for x:

x=d/(1-COS(L/(2*x)))

where L=28 and d=0.2


I have been able to get x~490 by "guessing" values for x and computing, then repeating until both sides are equal.

There must be a better way, although neither my TI-89 nor Mathematica are able to do it.
 
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It's unsolvable by algebraic methods. The best you can do is to use numerical techniques to get approximate values.
 
When I solve this numerically with Maple I get x = 1.0618829.
 

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