Solve \(6x^2 = 5x - 1\)

To solve the equation 6x^2 = 5x - 1, we first move all the terms to one side to obtain a quadratic equation in standard form, which is 6x^2 - 5x + 1 = 0. Then we can apply the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a, where a = 6, b = -5, and c = 1. Plugging these values into the quadratic formula, we get: x = (-(-5) ± sqrt((-5)^2 - 4(6)(1))) / 2(6) x = (5 ± sqrt(25 - 24)) / 12 x = (5 ± 1) / 12 Therefore, the solutions to the equation are x = 1/2 and x = 1/3. So the answer is x = 1/2, 1/3.