Find all numbers such that the square of the number is 48 more than double the number. If you find more than one, then list all the numbers you find in increasing order, separated by commas.?

-6, 8

Step-by-step explanation:

Let the numbers be represented by y

Square of y = y^2

Double y = 2 * y = 2y

Square of the number is 48 more than double the number is written mathematically as

y^2 = 2y + 48

y^2 - 2y - 48 = 0

This is a quadratic equation and can be solved by method of factorisation

y^2 - 2y - 48 = 0

y^2 + 6y - 8y - 48 = 0

(y^2 + 6y) - (8y - 48) = 0

y (y + 6) - 8 (y + 6) = 0

(y + 6) (y - 8) = 0

y = - 6, 8

The numbers are - 6, 8