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Solving a function with sinh

  1. Jun 3, 2009 #1
    I have the following equation:

    [tex]2a \sinh(\frac{25}{a}) = 51[/tex]

    How do I solve this for a?

    I tried changing it to:

    [tex]a(e^{\frac{25}{a}} - e^{\frac{-25}{a}}) = 51[/tex], but that didn't get me any further. Anyone?
  2. jcsd
  3. Jun 3, 2009 #2


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    Well, if it weren't for that overall multiplicative factor of [itex]a[/itex] on the LHS, you could multiply both sides by e^(25/a) to get a quadratic equation in terms of e^(25/a). But, that [itex]a[/itex] ruins everything, leaving you with a transcendental equation that I'm afraid you'll have to solve numerically (or perhaps in terms of the lambert W function), I believe.
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