Exponential - quadratic equation

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The equation 2n = n² has solutions at n = 2 and n = 4, with a third solution approximately at n = -0.767. The Lambert W function is suggested as a method for solving the equation without guessing. The discussion highlights the challenge of finding solutions analytically rather than through trial and error. Understanding the Lambert W function can provide deeper insights into solving such equations. Overall, the conversation emphasizes the importance of exploring advanced mathematical functions for solving nonlinear equations.
Tom83B
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Homework Statement



2n=n2

Homework Equations





The Attempt at a Solution



I know the solution is 2 and 4. But I have no idea how to solve it without guessing...
 
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Try looking at the LambertW function :) There's actually a third solution apart from the two you already found, its about -0.767
 

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