SOLUTION: I need help solving this! (20-x)/x = x

Question 708646: I need help solving this!
(20-x)/x = x
Answer by josh_jordan(263) (Show Source): You can put this solution on YOUR website!
In order to solve, we must first multiply both sides of our equation by x, to get rid of the fraction on the left side of the equal sign. Doing so gives us:

Next, we want to subtract everything on the left side of the equal sign, and place on the right side of the equal sign. This gives us:

We now have a quadratic equation. Let's see if we can solve by factoring, since it's a fast method. To do so, since the coefficient in front of is 1, we need to figure out what two numbers, when multiplied together, give us -20, and when added together, give us 1 (since the coefficient in front of the x is 1. Let's run through some of these numbers:

1 x -20 = -20; 1 + -20 = -19 DOESN'T WORK
-1 x 20 = -20; -1 + 20 = 19 DOESN'T WORK
2 x -10 = -20; 2 + -10 = -8 DOESN'T WORK
-2 x 10 = -20; -2 + 10 = 8 DOESN'T WORK
4 x -5 = -20; 4 + -5 = -1 DOESN'T WORK
-4 x 5 = -20; -4 + 5 = 1 WORKS!!!

We will put each of these numbers in factor form: (x - 4)(x + 5) = 0 Now, set each of these equal to 0, to solve for x: x - 4 = 0 ---> x = 4; x + 5 = 0 ---> x = -5. Therefore, our final answer is: 4, -5. Validate by plugging each number in the original equation.

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