SOLUTION: Six less than the product of two consecutive positive integers is equal to six times their sum. Find the two integers.

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Question 953313: Six less than the product of two consecutive positive integers is equal to six times their sum. Find the two integers.
Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
n=first number; n+1=second number
((n)(n+1))-6=6(n+n+1)
n^2+n-6=6(2n+1)
n^2+n-6=12n+6 Subtract (12n+6) from each side.
n^2-11n-12=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=169 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 12, -1. Here's your graph:

ANSWER 1: The first positive integer is 12.
x+1=12+1=13 ANSWER 2: The second positive integer is 13.
CHECK:
(12*13)-6=6(12+13)
156-6=6(25)
150=150
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