Ответ: \[a = 6:\] \[2a^{2} - 13 = 2 \cdot 6^{2} - 13 =\] \[= 2 \cdot 6 \cdot 6 - 13 = 12 \cdot 6 - 13 =\] \[= 72 - 13 = 59.\]