[tex]\Large\mathsf\displaystyle{} {3x}^{2} - 15x + 18 = 82 \\\\ \Large\mathsf\displaystyle{} {3x}^{2} - 15x + 18 - 82 = 0 \\\Large\mathsf\displaystyle{} {3x}^{2} - 15x - 64 = 0 \\\\ \Large\mathsf\displaystyle{} \begin{cases}a = 3 \\ b = - 15 \\ c = - 64\end{cases} \\\\ \Large\mathsf\displaystyle{}x = \dfrac{ - \left( - 15\right) \pm \sqrt{\left( - 15\right) ^{2} - 4\cdot3\cdot\left( - 64\right)} }{2\cdot3} \\\\\\ \Large\mathsf\displaystyle{}x = \dfrac{15 \pm \sqrt{255 + 768} }{6} \\\\\\ \Large\mathsf\displaystyle{}x = \dfrac{15 \pm \sqrt{993} }{6} \\\\\\ \Large\mathsf\displaystyle{}x = \dfrac{15 + \sqrt{993} }{6} \\\\ \Large\mathsf\displaystyle{}x = \dfrac{15 - \sqrt{993} }{6} \\\\ [/tex]

Solução:

[tex]\Large\displaystyle\text{$\begin{gathered} \underline{\boxed{\boldsymbol{ x_{1} = \dfrac{15 - \sqrt{993} }{6} }}}\end{gathered}$} [/tex]

[tex]\Large\displaystyle\text{$\begin{gathered} \underline{\boxed{\boldsymbol{ x_{2} = \frac{15 + \sqrt{993} }{6} }}}\end{gathered}$} [/tex]

[tex]\displaystyle\text{$\begin{gathered} \underline{\boxed{\boldsymbol{{ \red{Bons}} \blue{\:Estudos}}}}\end{gathered}$} [/tex]