SOLUTION: when the square of three times a positive integer is decreased by the integer, the result is 2010. what is the integer?

Question 530727: when the square of three times a positive integer is decreased by the integer, the result is 2010. what is the integer?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
x = a positive integer
3x = 3 times the number
9x^2 = the square of 3 times the number
.
9x^2-x = 2010
.
9x^2 -x -2010 = 0
.
Using the quadratic equation, we find:
.

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=72361 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 15, -14.8888888888889. Here's your graph:

.
So x = 15 is the only integer solution.
.
Checking this value, we find:
9*225 -15 = 2010
correct.
.
Answer: x = 15.
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