Verified answer

Multiply both sides by 6x.

x + 12 = x²

Subtract (x + 12x) from both sides.

0 = x² − x − 12

which if written in a more familiar form,

x² − x − 12 = 0

Now we have the quadratic equation we all learned about, with a = 1, b = −1, and c = −12. We can factor it and get (x + 3)(x − 4) = 0.

So, x = −3, +4.

I think that this equation actually has two roots.

1/6 + 2/x = x/6

The first thing you have to do is on the Left side, so that the denominator of both components is the same.

1/6 + 2/x:

multiply the first term by x and the second term by 6 (in other words, multiply each term by the other one's denominator).

Then you'll have

x/6x + 12/6x = x/6

x + 12 = x

- -- -

6x 6x 6

Now cross multiply:

6(x + 12) = x(6x)

6x + 72 = 6 x^2

divide everything through by 6 to simplify everything:

x + 12 = x^2

Now arrange it as a quadratic equation that you can solve:

0 = x^2 - x - 12

The two roots of this equation are:

x = 4 and x = -3.

Both of these numbers satisfy your original equation if you plug them into it.

Hope this was helpful.

1/6+2/x=x/6

1+12/x=x

12/x=x-1

12=x^2-x

I can't exactly remember how to break that down further I'll think on it and if I can I'll post that but you eventually reach that

x=4.