Question

The product of two consecutive numbers is 14 less than 10 times the smaller number. find each number

Answer 1

The consecutive numbers are either 2 and 3, or 7 and 8..

x(x+1) = x^2 + x 
x^2 + x = 10x-14

quadratic form of x^2 + x = 10x-14:
x^2 - 9x + 14 = 0

(x-2)(x-7) = 0

x = 2, 7

so 2 and 3, or 7 and 8 are the answers