Find three consecutive integers such that the product of the first and third is 5 greater than 5 times the second.

Step-by-step explanation:

3 consecutive integers ...

1st integer = x

2nd integer = x + 1

3rd integer = x + 2

the product of 1st and 3rd is 5 greater then 5 times the 2nd ...

x (x+2) = 5 (x + 1) + 5

x^2 + 2x = 5x + 5 + 5

x^2 + 2x = 5x + 10

x^2 + 2x - 5x - 10 = 0

x^2 - 3x - 10 = 0

(x - 5) (x + 2) = 0

x - 5 = 0 x + 2 = 0

x = 5 x = - 2

so it will be : 5,6, and 7 or - 2,-1, and 0