Explanation:
as we know that 81 = 9², therefore -81 = -9×9,
and 9 = -9 + 18, the numbers are
9 and -9.
but let's do it formally too :
x = y + 18
x × y = -81
let's use the first (identity) in the second equation :
(y + 18) × y = -81
y² + 18y = -81
y² + 18y + 81 = 0
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = y
a = 1
b = 18
c = 81
y = (-18 ± sqrt(18² - 4×1×81))/(2×1) =
= (-18 ± sqrt(324 - 324))/2 = (-18 ± 0)/2 = -9
x = y + 18 = -9 + 18 = 9
we see we get the same result, of course.