$$\DeclareMathOperator{\abs}{abs} \newcommand{\ensuremath}[1]{\mbox{#1}}$$
$\tag{cubic1}\label{cubic1}{{x}^{3}}-3{{x}^{2}}-2x+5=0$
$\tag{cubic2}\label{cubic2}{{x}^{3}}-3x-1=0$
$\tag{\%{}o4}\label{o4} [x=\frac{2\sqrt{5}\,\cos{\left( \frac{\operatorname{atan}\left( \frac{\sqrt{473}}{{{3}^{\frac{3}{2}}}}\right) -3\ensuremath{\pi} }{3}\right) }+\sqrt{3}}{\sqrt{3}},x=\frac{2\sqrt{5}\,\cos{\left( \frac{\operatorname{atan}\left( \frac{\sqrt{473}}{{{3}^{\frac{3}{2}}}}\right) -\ensuremath{\pi} }{3}\right) }+\sqrt{3}}{\sqrt{3}},x=\frac{2\sqrt{5}\,\cos{\left( \frac{\operatorname{atan}\left( \frac{\sqrt{473}}{{{3}^{\frac{3}{2}}}}\right) +\ensuremath{\pi} }{3}\right) }+\sqrt{3}}{\sqrt{3}}]$
$\tag{\%{}o5}\label{o5} [x=2\cos{\left( \frac{\ensuremath{\pi} }{9}\right) },x=2\cos{\left( \frac{5\ensuremath{\pi} }{9}\right) },x=2\cos{\left( \frac{7\ensuremath{\pi} }{9}\right) }]$
$\tag{sextic}\label{sextic}{{x}^{6}}-3{{x}^{5}}-5{{x}^{4}}+13{{x}^{3}}+9{{x}^{2}}-13x-5=0$
$\tag{\%{}o7}\label{o7} [x=2\cos{\left( \frac{\ensuremath{\pi} }{9}\right) },x=2\cos{\left( \frac{5\ensuremath{\pi} }{9}\right) },x=2\cos{\left( \frac{7\ensuremath{\pi} }{9}\right) },x=\frac{2\sqrt{5}\,\cos{\left( \frac{\operatorname{atan}\left( \frac{\sqrt{473}}{{{3}^{\frac{3}{2}}}}\right) -3\ensuremath{\pi} }{3}\right) }+\sqrt{3}}{\sqrt{3}},x=\frac{2\sqrt{5}\,\cos{\left( \frac{\operatorname{atan}\left( \frac{\sqrt{473}}{{{3}^{\frac{3}{2}}}}\right) -\ensuremath{\pi} }{3}\right) }+\sqrt{3}}{\sqrt{3}},x=\frac{2\sqrt{5}\,\cos{\left( \frac{\operatorname{atan}\left( \frac{\sqrt{473}}{{{3}^{\frac{3}{2}}}}\right) +\ensuremath{\pi} }{3}\right) }+\sqrt{3}}{\sqrt{3}}]$