Answer: \(m = 2\) or \(m = -\dfrac{5}{3}\)
Comparing with \(am^2 + bm + c = 0\): \(a = 3\), \(b = -1\), \(c = -10\).
\(b^2 - 4ac = (-1)^2 - 4(3)(-10) = 1 + 120 = 121\)
\(m = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \dfrac{1 \pm 11}{6}\)
\(m = \dfrac{1 + 11}{6} = 2\) or \(m = \dfrac{1 - 11}{6} = -\dfrac{10}{6} = -\dfrac{5}{3}\).