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

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Question 177035: Solve equations
x/3 = 4/x+1
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-3/x = x/-3
Answer by nerdybill(7384) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-3x%2B-12+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-3%29%5E2-4%2A1%2A-12=57.

Discriminant d=57 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+57+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+57+%29%29%2F2%5C1+=+5.27491721763537
x%5B2%5D+=+%28-%28-3%29-sqrt%28+57+%29%29%2F2%5C1+=+-2.27491721763537

Quadratic expression 1x%5E2%2B-3x%2B-12 can be factored:
1x%5E2%2B-3x%2B-12+=+1%28x-5.27491721763537%29%2A%28x--2.27491721763537%29
Again, the answer is: 5.27491721763537, -2.27491721763537. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-3%2Ax%2B-12+%29


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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}