SOLUTION: Please help me solve this equation and check my solution. {{{ 18/(x-3) = x/3 }}} Sorry I didn't know how to put the line under the numerator!!!

Question 75030This question is from textbook
: Please help me solve this equation and check my solution.
Sorry I didn't know how to put the line under the numerator!!! This question is from textbook

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To make a fraction of just place 18/(x-3) in triple curly brackets.
Start with the given problem
Multiply both sides by 3, this eliminates the denominator of the right side
Multiply both sides by (x-3), this eliminates the denominator of the left side
So we're left with this:

Distribute the x
Subtract 54 from both sides
Factor the right side

There's one answer

There's the other answer
So the solution is x=9 and x=-6

Check:
Plug in x=9

works
Plug in x=-6

works
Here's another way to solve it:
When you have the quadratic , plug the coefficients into the quadratic formula:

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=225 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 9, -6. Here's your graph:

And you see the same answer, but it's just another way to get there.
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