SOLUTION: Can you please show me how to solve the following equation. We are not solving for x, but for all solutions. x/x-1+8/x=10/4

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Question 681678: Can you please show me how to solve the following equation. We are not solving for x, but for all solutions.
x/x-1+8/x=10/4
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Can you please show me how to solve the following equation. We are not solving for x, but for all solutions.
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x is the only variable, the only thing to solve for.
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x/(x-1) + 8/x = 10/4 = 5/2
Mutliply by 2x(x-1)
2x*x + 8*2*(x-1) = 5x*(x-1)


Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
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=249 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 6.12995563967658, 0.870044360323417. Here's your graph:
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