The domain of a radical function is all real numbers for which the radicand (the expression under the radical) is greater than or equal to zero. So in order to find the domain of $f(x)=\sqrt{2x^2-3x-20}$, we need to solve the inequality $2x^2-3x-20\ge 0$.
We can start by factoring the radicand:
```
2x^2-3x-20 = (2x+5)(x-4)
```
So the inequality becomes:
```
(2x+5)(x-4)\ge 0
```
This inequality is true when either $2x+5\ge 0$ or $x-4\ge 0$. Solving these inequalities, we get:
```
x\ge -\frac52 \text{ or } x\ge 4
```
Putting these two restrictions together, we get that the domain of $f(x)$ is the set of all real numbers $x$ such that $x\ge -\frac52$ or $x\ge 4$. This can be written in mathematical notation as:
```
D = \left\{ x \in \RR \mid x\ge -\frac52 \text{ or } x\ge 4 \right\}
```
In interval notation, this is:
```
D = \boxed{\left[ -\frac52, \infty \right)}
```