(c) $2 x^{2}-2 x-5=0$

Step 1 ：Solve the quadratic equation \(2x^2 - 2x - 5 = 0\) using the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\) where a = 2, b = -2, and c = -5.

Step 2 ：Calculate the discriminant: \(D = b^2 - 4ac = 44\)

Step 3 ：Find the solutions for x: \(x_1 \approx 1.618\) and \(x_2 \approx -1.618\)

Step 4 ：\(\boxed{x_1 \approx 1.618, x_2 \approx -1.618}\)