SOLUTION: Solve equations x/3 = 4/x+1 -----------

SOLUTION: Solve equations x/3 = 4/x+1 ----------- - -3/x = x/-3

Question 177035: Solve equations
x/3 = 4/x+1
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-3/x = x/-3
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
x/3 = 4/x+1
Multiply both sides by 3x:
x^2 = 12+3x
Move all terms to the left:
x^2-3x-12=0
Since you can't factor, you must apply the quadratic equation. Doing so, yields:
x={5.2749, -2.2749}
Here's the details of the quadratic:

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=57 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 5.27491721763537, -2.27491721763537. Here's your graph:

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-3/x = x/-3
Multiply both sides by -3x:
9 = x^2
Taking the square root of both sides:
x = {-3,3}