What two consecutive even numbers has a product of 360?

Let one of the number be y and other be y+2

According to question:

y(y+2) = 360

y2 + 2y = 360

y2 + 2y - 360 = 0

which is of the form ay2 + by + c = 0

Value of y can be calculated using the formula: y = {-b ± (b2 - 4ac)1/2}/2a

Here a = 1, b = 2 and c = -360

Putting these values in the formula:

y = {-2 ± (22 - 4x1x-360)1/2}/2x1 = {-2 ± (4 + 1440)1/2}/2 = {-2 ± 38}/2

y = (-2 + 38)/2 = 18 or y = (-2 - 38)/2 = -20

If y = 18 then the other number = y + 2 = 20

If y = -20 then the other number = y + 2 = -18

So, we have two solutions (18, 20) and (-20, -18).