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Let your numbers be x and y. We're told:
x + y = 6
x * y = 135
Let's take the second equation and plug it into the first one:
x + (135 / x) = 6
∴ x2 +135 = 6x
∴ x2 - 6x = -135
∴ x2 - 6x + 9 = -144
∴ (x - 3)2 = -144
∴ x - 3 = ± 12i
∴ x = 3 ± 12i