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I want to solve the following equation

2 x == Sinh[x]

Mathematica is unable to do so

In[1]:= Solve[2 x == Sinh[x], x]
During evaluation of In[20]:= Solve::nsmet: This system cannot be solved with the methods available to Solve. >>
Out[1]= Solve[2 x == Sinh[x], x]

However, Wolfram|Alpha can successfully solve the equation

Wolfram|Alpha query

How can I achieve the same in Mathematica?

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    $\begingroup$ Try Solve[2 x == Sinh[x], x, Reals]. This is a common question - here's a similar example. $\endgroup$ – Mark McClure Jul 21 '14 at 23:46
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    $\begingroup$ You didn't ask Mathematica for a numerical solution, you asked for a symbolic one. $\endgroup$ – m_goldberg Jul 21 '14 at 23:53
  • $\begingroup$ If I ask Mathematica for a numerical solution, using NSolve, it gives me the same error, though. $\endgroup$ – Gregger Jul 21 '14 at 23:55
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    $\begingroup$ @Sven86, Use NSolve[2 x == Sinh[x], x, Reals]. NSolve has a default domain of Complexes just like Solve. $\endgroup$ – Chip Hurst Jul 22 '14 at 0:43
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Plot[2 x - Sinh[x], {x, -Pi, Pi}]

enter image description here

FindRoot[2 x == Sinh[x], {x, #}] & /@ {-2, 0, 2}

{{x -> -2.17732}, {x -> 0.}, {x -> 2.17732}}
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  • 1
    $\begingroup$ @Sven86 This syntax also works, though I believe it is undocumented: FindRoot[2 x == Sinh[x], {x, {-2, 0, 2}}]. Note that the output form is different: {x -> {-2.17732, 0., 2.17732}}. $\endgroup$ – Mr.Wizard Jul 22 '14 at 17:33

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