Not sure how to go about this question...
How many solutions does the equation -6 sinh(x) = 9 have?
Thanks.
Easiet way is to graph $\displaystyle y = \sinh x\;\;\; \text{and}\;\;\; y = -\frac {3}{2}$ and look for intersection points. To find them, replace
$\displaystyle \sinh x = \frac{e^x - e^{-x}}{2}$
so
$\displaystyle \frac{e^x - e^{-x}}{2} = -\frac{3}{2}$
or
$\displaystyle e^x + 3 - e^{-x} = 0 $
or
$\displaystyle \left(e^x\right)^2 + 3 e^x - 1 = 0 $
Now this is a quadratic in $\displaystyle e^x$. Yours from here.