How to calculate the 3dB point?

The answer to your first question comes from a little algebra. Subtract 7 from both sides, divide by 1.579e-5, and take the square root:

$$sqrt{frac{27.8766 - 7}{1.579times10^{-5}}} = 1149.8$$

The conversion to radians per second is done by multiplying by $2pi$ as they show.

To answer your follow up question about where $1.579times10^{-5}$ comes from, it is equal to the expression from earlier in the same line, after factoring $(2pi f_{6dB})^2$ into $(2pi)^2(f_{6dB})^2$:

$$(4times10^{-7})cdot(2pi)^2$$