3.48: Tangent to an exponential curve

A curve has equation $y=5\mathrm{e}^{x}+\mathrm{e}^{-x}$. The tangent to the curve at the point where $x=1$ cuts the $x$-axis at the point $P$. Find the equation of the tangent in the form $y=mx+c$, where $m$ and $c$ are exact, and hence find the $x$-coordinate of $P$.