# Thread: 5 coshx + 4 sinh x =7

1. ## 5 coshx + 4 sinh x =7

I need help solving this equation

5 coshx + 4 sinh x =7

Any help would be greatly appreciated. Cheers!

2. Originally Posted by taichi2910
I need help solving this equation

5 coshx + 4 sinh x =7

Any help would be greatly appreciated. Cheers!
Using the definition of cosh and sinh will help simpilfy the problem

$5\left( \frac{e^{x}+e^{-x}}{2}\right)+4\left( \frac{e^{x}-e^{-x}}{2}\right)=7 \implies$

$9e^{x}+e^{-x}=14$

Now this is quadratic in form if we multiply by $e^{x}$ we get

$9(e^{x})^2+1=14e^{x} \iff 9(e^{x})^2-14e^{x}+1=0$

To simplify things let $u=e^{x}$

$9u^2-14u+1=0$

You should be able to finish from here. Good luck