Hint:

\(\displaystyle{\frac{{{5}{{\sin}^{{2}}{x}}}}{{{{\cos}^{{2}}{x}}}}}+{\frac{{{8}{\sin{{x}}}}}{{{\cos{{x}}}}}}-{\frac{{{3}{{\sin}^{{2}}{x}}+{3}{{\cos}^{{2}}{x}}}}{{{{\cos}^{{2}}{x}}}}}={0}\)

\(\displaystyle{2}{{\tan}^{{2}}{x}}+{8}{\tan{{x}}}-{3}={0}\)

\(\displaystyle{\frac{{{5}{{\sin}^{{2}}{x}}}}{{{{\cos}^{{2}}{x}}}}}+{\frac{{{8}{\sin{{x}}}}}{{{\cos{{x}}}}}}-{\frac{{{3}{{\sin}^{{2}}{x}}+{3}{{\cos}^{{2}}{x}}}}{{{{\cos}^{{2}}{x}}}}}={0}\)

\(\displaystyle{2}{{\tan}^{{2}}{x}}+{8}{\tan{{x}}}-{3}={0}\)