Finding the Root of a Transcendental Equation with Sinh

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The equation 2a sinh(25/a) = 51 presents a challenge for finding the variable a. Attempts to manipulate the equation into a quadratic form using exponential functions were unsuccessful due to the presence of the multiplicative factor a. This results in a transcendental equation that cannot be solved algebraically. The recommended approaches include numerical methods or potentially using the Lambert W function for a solution. Ultimately, solving this equation requires advanced techniques beyond simple algebraic manipulation.
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I have the following equation:

2a \sinh(\frac{25}{a}) = 51

How do I solve this for a?

I tried changing it to:

a(e^{\frac{25}{a}} - e^{\frac{-25}{a}}) = 51, but that didn't get me any further. Anyone?
 
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Well, if it weren't for that overall multiplicative factor of a 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 a 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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