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If we call the two numbers x and y, we know that
xy = -420
and
x + y = 16.
Solving the second equation for y and substituting it into the first,...
y = 16 - x
x(16-x) = -420
-x² + 16x + 420 = 0
x² - 16x - 420 = 0
Substituting a, b and c into the quadratic equation and solving for x yeilds -14 and 30. Replacing x with -14 in either equation makes y = 30, and replacing x with 30 in either equation makes y = -14, so the two numbers are -14 and 30.
Or, you can look at the factors of 420 (2 x 2 x 3 x 5 x 7), then try combining them to find two that have a difference of 16.
Since the product is negative, the two numbers must have opposite signs, therefore you're looking for a difference: 30 = (2 x 3 x 5) & 14 = (2 x 7); 30 x 14 = 420, and 30 - 14 = 16, so the two numbers are 30 and negative 14.
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