Ответ: \[m = 8:\] \[2m^{2} - 9 = 2 \cdot 8^{2} - 9 =\] \[= 2 \cdot 8 \cdot 8 - 9 = 2 \cdot 64 - 9 =\] \[= 128 - 9 = 119.\]