#### Answer

$m=\dfrac{7}{6}\pm\dfrac{\sqrt{85}}{6}$

#### Work Step by Step

$3m^{2}-7m=3$
Take the $3$ to the left side of the equation:
$3m^{2}-7m-3=0$
Use the quadratic formula to solve the equation. The formula is $m=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=3$, $b=-7$ and $c=-3$
Substitute:
$m=\dfrac{-(-7)\pm\sqrt{(-7)^{2}-4(3)(-3)}}{2(3)}=\dfrac{7\pm\sqrt{49+36}}{6}=...$
$...=\dfrac{7\pm\sqrt{85}}{6}=\dfrac{7}{6}\pm\dfrac{\sqrt{85}}{6}$