Answer: \(m = \frac{-1 + \sqrt{22}}{3} \text{ or } \frac{-1 - \sqrt{22}}{3}\)
Compare with \(am^2 + bm + c = 0\): \(a = 3\), \(b = 2\), \(c = -7\).
\(b^2 - 4ac = 4 + 84 = 88\)
\(m = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
\[m = \frac{-2 \pm \sqrt{88}}{6} = \frac{-2 \pm 2\sqrt{22}}{6}\]\[m = \frac{-1 \pm \sqrt{22}}{3}\]