Answer
$\left\{ \dfrac{7-\sqrt{85}}{6},\dfrac{7+\sqrt{85}}{6} \right\}$
Work Step by Step
The standard form of the given equation, $
3m^2-7m=3
,$ is
\begin{array}{l}\require{cancel}
3m^2-7m-3=0
.\end{array}
Using $\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), the solutions of the quadratic equation, $
3m^2-7m-3=0
,$ are
\begin{array}{l}\require{cancel}
\dfrac{-(-7)\pm\sqrt{(-7)^2-4(3)(-3)}}{2(3)}
\\\\=
\dfrac{7\pm\sqrt{49+36}}{6}
\\\\=
\dfrac{7\pm\sqrt{85}}{6}
.\end{array}
Hence, the solutions are $
\left\{ \dfrac{7-\sqrt{85}}{6},\dfrac{7+\sqrt{85}}{6} \right\}
.$
