why is $O(n^2)$ equal to $n^{1.5}$? I am learning this MIT course, which gives this formula

$$O(n^2) = n^{1.5}$$

is there a table to calculate this? like $O(n^{1.5})$, $O(n^{5})$ ?

what x takes would have O(x) give $c \cdot n$  where c is a constant,
The formula is wrong. The notation $f = O(g)$ is asymmetric, and has the meaning $f \in O(g)$. For more, check our reference question on Landau notation. Other relevant reference questions are this one and this one.