Answer
There is no real solution.
Work Step by Step
Solve the provided equation,
$\begin{align}
& 2\cos x-1+3\sec x=0 \\
& 2\operatorname{cosx}+3\frac{1}{\cos x}=1 \\
& \frac{2{{\cos }^{2}}x+3}{\cos x}=1 \\
& 2{{\cos }^{2}}x+3-\cos x=0
\end{align}$
And use the quadratic formula, $\cos x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$
$\begin{align}
& 2{{\cos }^{2}}x-\cos x+3=0 \\
& \cos x=\frac{1\pm \sqrt{1-4\left( 2 \right)\left( 3 \right)}}{2\left( 2 \right)} \\
& \cos x=\frac{1\pm \sqrt{-11}}{4}
\end{align}$
Thus, there is no real solution for the provided equation.
