Solving Exponential and Hyperbolic Equations: e^(3x)+sinh(x)=0

[System]

Homework Statement

Solve the following equation for x:

$$e^{3x}+sinh(x)=0$$

Homework Equations

None.

The Attempt at a Solution

It the same as:

$$e^{3x}+\frac{e^{2x}}{2}-\frac{e^{-2x}}{2}=0$$

Multiply by 2

$$2e^{3x}+e^{2x}-e^{-2x}=0$$

Multiply by e^(2x)

$$2e^{5x}+e^{4x}=1$$

then I stopped.

 

[Karmalo]

I think $$sinh(x)=\frac{e^{x}}{2}-\frac{e^{-x}}{2}$$

 

[niklaus]

sinh(x) = 1/2(e^x - e^(-x))

Looks to me like you should be able to get a quadratic equation out of that...

 

[System]

ohhhh
sorry
:|
I finished it
thanks <3