With long equations, it is probably best by far to just write it out and say "this equation". Nevertheless, I think it is worth noting that there is a way to say equations like this out loud, and in principle it should work for any equation. For example, many of us were taught to memorize the quadratic formula in middle school:
$$
x = \frac{- b \pm \sqrt{b^2 - 4ac}}{2a}
$$
"x is equal to the opposite of b, plus or minus
the square root of quantity b squared minus four a c,
all over two a."
Here's a transcription of the formula you mentioned:
$$
\left(D + \frac{b}{2m} - \sqrt{\frac{b^2}{4 m^2} - \omega_0^2} \right) \left(D + \frac{b}{2m} + \sqrt{\frac{b^2}{4 m^2} - \omega_0^2}\right) y = 0
$$
"The quantity capital d plus b over two m minus the square root of the quantity b squared over four m squared minus omega naught squared, end quantity, end quantity, all times the quantity capital d plus b over two m plus the square root of the quantity b squared over four m squared minus omega naught squared, end quantity, end quantity, times y, is equal to zero."
Obviously, there are some order of operations issues and a lot of potential for ambiguity, but using "quantity...end quantity" in theory can remove all such ambiguity. The order can also often be discerned from the context.
As an alternative to "quantity...end quantity", in casual speech with friends I have noticed a common practice of using longer spaces to indicate order. This often comes up in distinguishing $x_n + 1$ and $x_{n+1}$; the first is usually voiced as "x sub n [pause] plus 1" while the second is voiced as "x sub [pause] n-plus-one".
