Answer: \(m = \frac{2 + \sqrt{14}}{5} \text{ or } \frac{2 - \sqrt{14}}{5}\)
Compare with \(am^2 + bm + c = 0\): \(a = 5\), \(b = -4\), \(c = -2\).
\(b^2 - 4ac = 16 + 40 = 56\)
\(m = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
\[m = \frac{4 \pm \sqrt{56}}{10} = \frac{4 \pm 2\sqrt{14}}{10}\]\[m = \frac{2 \pm \sqrt{14}}{5}\]