2017/029) Find the exact value for the real root of the equation $x^3+3x-2=0$

Say $f(x)=x3+3x-2=0$
$f(x)$  changes sign once so there is one positive root.
$f(-x)=-x^3-3x-2$ changes sign zero times so no -ve root
let $x=2sinh\, t$
so $ x^3+3x=2=>8\sinh\,3t+6sinh\,t=2$
or $4sinh\,3t+3sinh\,t=1$
or $sinh\,3t=1$ or $3t=sinh^{-1}1$
hence $x=2sinh(\frac{sinh^{-1}}{3})x$
this is the only real root