\( \begin{array}{c}\sqrt{5 x^{2}-6 x+8}-\sqrt{5 x^{2}-6 x-7}=1 \\ x=?\end{array} \)
\(x = \frac{6 \pm \sqrt{316}}{10}\)
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 :\(x = \frac{6 \pm \sqrt{316}}{10}\)