Answer
$x=arccos\frac{1}{4}+2n\pi$, where $n$ is an integer.
Work Step by Step
$sec^2x-4~sec~x=0$
$sec~x(sec~x-4)=0$
$sec~x=0$. But, there is no $x$ such that $sec~x=0$.
$sec~x-4=0$
$sec~x=4$
$\frac{1}{cos~x}=4$
$cos~x=\frac{1}{4}$
$x=arccos\frac{1}{4}$
The period of $cos~x$ is $2\pi$. So, add multiples of $2\pi$ to each solution to find the general solution:
$x=arccos\frac{1}{4}+2n\pi$, where $n$ is an integer.
