Finding the Root of a Transcendental Equation with Sinh

[Shukie]

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?

 

[Mute]

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.