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To find two numbers that multiply to -51 and add to -14, we need to solve a system of equations. Let's call the two numbers x and y. We have the equations xy = -51 and x + y = -14. By substituting y = -14 - x into the first equation, we get x(-14 - x) = -51. Simplifying this quadratic equation gives us x^2 + 14x - 51 = 0. Solving for x using the quadratic formula, we find x = 3 and x = -17. Therefore, the two numbers are 3 and -17.