Answer
$x=-2.17$
Work Step by Step
$f(x)=3x^{3}-10x+9=0$
Work shown in image below.
Subdivide the interval $[-3,-2]$ into 10 subintervals and find f(each endpoint).
We find opposite signs on endpoints of $[-2.2,-2.1 ]$.
By the Intermediate Value Theorem, a real zero is inside that interval.
Subdivide the interval $[-2.2,-2.1 ]$ into 10 subintervals and find f(each endpoint).
We find opposite signs on endpoints of $[-2.18,-2.17]$.
So a real zero is $x=-2.17...$
Correct to 2 decimal places : $x=-2.17$