Can this equation be solved algebraically?

[seeker]

I know how to solve an equation whose unknown is part of an exponent, however if that unknown also appears elsewhere, can you still solve it algebraically? Or must it be solved numerically, using Newton's clever algorithm? Here is the equation that has stymied me:
22=(9.8/x)*(1-e^(-3x))
If it can be solved algebraically, please be very specific about the steps, if you don't mind.

 

[Deleted member 4993]

I know how to solve an equation whose unknown is part of an exponent, however if that unknown also appears elsewhere, can you still solve it algebraically? Or must it be solved numerically, using Newton's clever algorithm? Here is the equation that has stymied me:


\(\displaystyle 22\, = \, \frac{9.8}{x} \, \cdot (1-e^{-3x})\)<<<< I don't see any closed-form algebraic method of solution

If it can be solved algebraically, please be very specific about the steps, if you don't mind.

 

[seeker]

Thank you for your response, Mr. Khan. May I request a tiny clarification? You used the term closed-form algebraic solution-- am I correct that this would include all sorts of logarithmic manipulations? Is my suspicion correct then, that only a numerical solution is possible, or is there some additional category, beyond closed form algebraic and numerical? And is Newton's algorithm the only numerical method, or have better ones been devised? And by the way, how does a computer program know where to begin the algorithm, how does it estimate the appropriate place for the first iteration?