Can someone explain how to solve for x?
I know it'll be put into a quadratic equation and x will have two solutions. I just don't know how to set it up.

\frac{2x^2}{2x^2 + 24x} = frac{2}{x}

Question

Can someone explain how to solve for x? 
I know it'll be put into a quadratic equation and x will have two solutions. I just don't know how to set it up. 

\frac{2x^2}{2x^2 + 24x} = frac{2}{x}

anonymous · Answer

Uh. It didn't work.

$$\frac{2x^2}{2x^2 + 24x} = \frac{2}{x}$$

anonymous · Answer

@SWAG @Luis_Rivera @ganeshie8

anonymous · Answer

I did that and got 

$$2x^3 = 4x^2 + 48x$$

anonymous · Answer

Clearly the above isn't a quadratic. I'm so confused.

anonymous · Answer

i mean

anonymous · Answer

|dw:1368652195677:dw|

anonymous · Answer

Wait, so my xs canceled out? Can you show me using the Equation editor? I understand better that way.

amistre64 · Answer

$$\frac{2x^2}{2x^2 + 24x} = \frac{2}{x}$$
$$2x^2(x) = 2(2x^2 + 24x)$$
$$2x^3 = 4x^2 + 48x$$
$$2x^3 - 4x^2 - 48x=0$$factor our a 2x
$$2x(x^2 - 2x - 24)=0$$

amistre64 · Answer

there are at most 3 solutions to the setup that would have to be verified afterwards

amistre64 · Answer

essentially:

2x = 0, when x = 0

x^2 -2x -24 = 0, when x = ... use the quadratic formula as instructed

anonymous · Answer

Oh, okay, thanks:)

anonymous · Answer

So I got it down to 4x( x^2 - 4x + 4) 

However, I ran into a problem. 

When I plug it into the quadratic equation none of my answers match the answers on the test.