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:

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

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

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

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