\( \begin{array}{c}\sqrt{5 x^{2}-6 x+8}-\sqrt{5 x^{2}-6 x-7}=1 \\ x=?\end{array} \)

Step 1 ：\( \sqrt{5 x^{2}-6 x+8} = \sqrt{5 x^{2}-6 x-7} + 1 \)

Step 2 ：\( 5 x^{2}-6 x+8 = (5 x^{2}-6 x-7) + 2\sqrt{(5 x^{2}-6 x-7)} + 1\)

Step 3 ：\(0 = 14 + 2\sqrt{(5 x^{2}-6 x-7)}\)

Step 4 ：\(\sqrt{(5 x^{2}-6 x-7)} = -7\)

Step 5 ：\(5 x^{2}-6 x-7 = 49\)

Step 6 ：\(5 x^{2}-6 x-56 = 0\)

Step 7 ：\(x = \frac{6 \pm \sqrt{(-6)^2-4 \cdot 5 \cdot (-56)}}{2 \cdot 5}\)

Step 8 ：\(x = \frac{6 \pm \sqrt{316}}{10}\)