It amounts to solving it backwards: Start with the solutions: x = -1/3; x = 5/2 Clear of fractions: 3x = -1; 2x = 5 Get 0 on the right of each: 3x+1 = 0; 2x-5 = 0 Multiply equals by equals: (3x+1)(2x-5) = 0 Foil that out: 6x²-15x+2x-5 = 0 6x²-13x+5 = 0 That's the quadratic equation. Edwin