\(\displaystyle{\tan{{\left({x}\right)}}}+√{3}={0}\)

Subtract \(\displaystyle√{3}\) from both sides

\(\displaystyle{\tan{{\left({x}\right)}}}+√{3}-√{3}={0}-√{3}\)

\(\displaystyle{\tan{{\left({x}\right)}}}=-√{3}\)

General solution for \(\displaystyle{\tan{{\left({x}\right)}}}=-√{3}\) \(\displaystyle{x}={2}\frac{{\pi}}{{3}}+{\left(\pi\right)}{n}\)

[Radians: \(\displaystyle{x}={2}\frac{{\pi}}{{3}}+{\left(\pi\right)}{n};{D}{e}{g}{r}{e}{e}{s}:{x}={120}+{180}{n}{]}\)

Subtract \(\displaystyle√{3}\) from both sides

\(\displaystyle{\tan{{\left({x}\right)}}}+√{3}-√{3}={0}-√{3}\)

\(\displaystyle{\tan{{\left({x}\right)}}}=-√{3}\)

General solution for \(\displaystyle{\tan{{\left({x}\right)}}}=-√{3}\) \(\displaystyle{x}={2}\frac{{\pi}}{{3}}+{\left(\pi\right)}{n}\)

[Radians: \(\displaystyle{x}={2}\frac{{\pi}}{{3}}+{\left(\pi\right)}{n};{D}{e}{g}{r}{e}{e}{s}:{x}={120}+{180}{n}{]}\)