Answer
$x=2.13$
Work Step by Step
We test $f(x)=3x^{3}-2x^{2}-20$
on nonnegative integer values of x, and find that
$f(2) $is negative, $f(3)$ is positive $\Rightarrow$ by the IVT, a real zero is inside $[2,3].$
Subdividing $[2,3]$ into 10 subintervals, calculating f( endpoints), we find
$f(2.1) $is negative, $f(2.2)$ is positive $\Rightarrow$ by the IVT, a real zero is inside $[2.1,2.2].$
Subdividing again, we find
$f(2.13) $is negative, $f(2.14)$ is positive $\Rightarrow$ by the IVT, a real zero is inside $[2.53,2.54].$
The real zero is $x=2.13...$
To two decimal places, $x=2.13$