Here are the steps to solve this quadratic equation using the quadratic formula: 1. Identify the coefficients: a = 3, b = -1, c = -5/2 2. Plug the coefficients into the quadratic formula: x = (-b ± √(b2 - 4ac)) / 2a x = (-(-1) ± √((-1)2 - 4(3)(-5/2))) / 2(3) 3. Simplify: x = (1 ± √(1 + 30)) / 6 4. Evaluate the square root: x = (1 ± 5√3) / 6 Therefore, the solutions are: