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Solve the following equation?

Sabrina Lau
Posted 7 years ago
POSTED BY: Sabrina Lau
3 Replies
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E is exact. But .45 is not exact, it is a decimal approximation. One might instead use 9/20.
POSTED BY: Daniel Lichtblau 
 eq = -0.45 - 8./(1 + 3 E^(-x/30)) + (80 E^(-x/30) (0.65 - 0.01 x))/(1 + 3 E^(-x/30))^2;
 Solve[Rationalize[eq, 0] == 0, x, Reals]

 (*  {{x -> Root[{81 + 169 E^(#1/15) + 
        E^(#1/30) (-506 + 16 #1) &, -96.939605776733132399}]}, {x -> 
    Root[{81 + 169 E^(#1/15) + E^(#1/30) (-506 + 16 #1) &, 
      12.3348914426321591897}]}} *)

 NSolve[eq == 0, x, Reals]

 {{x -> -96.9396}, {x -> 12.3349}}

Or use FindRoot. 

 {FindRoot[eq, {x, 10}],FindRoot[eq, {x, -90}]}

  (* {{x -> 12.3349}, {x -> -96.9396}} *)
POSTED BY: Mariusz Iwaniuk

For trascendental equations it is useful to give a bounded interval where to search, for example:

Solve[-0.45 - 8./(1 + 3 E^(-x/30)) +
    (80 E^(-x/30) (0.65 - 0.01 x))/(1 + 3 E^(-x/30))^2 == 0 &&

  0 < x < 20,
 x]

I chose the interval 0 < x < 20 after plotting the function.
POSTED BY: Gianluca Gorni
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