Solving a formula of terms having a variable in their

I am having concerns addressing the list below formula : $$\frac{x}{2x-3} - \frac{1}{2x} = \frac{3}{4x-6}$$

The resolution of this is 1.

It remains in the area of parabolas and also it need to be rather very easy to address.

My actions are as adheres to :

$$\frac{x}{2x-3} - \frac{1}{2x} = \frac{3}{4x-6}$$ Multiply by $2x(4x-6)$

$$4x^2 -1(4x-6) = 6x$$ obtains me below, remove $6x$

$$4x^2 - 10x + 6 = 0$$

Solving this with the parabola formula I wound up obtaining $\{4,6\}$.

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2019-12-02 03:12:26
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@J. M. :

After looking into the formula I figured out that I separating by $2$ as opposed to $4a$/ $8$

$$\frac{10 \pm \sqrt{100-96}}{2}$$

With the set kind I get the outcomes $1.5$ and also $1$ of which $1$ is matching outcome.

Many thanks for the kind assistance!

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2019-12-03 05:07:43
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HINT $\rm\displaystyle\quad \frac{1}{2\ x}\ =\ \frac{2\ x}{4\ x-6} - \frac{3}{4\ x-6}\ =\ \frac{1}2\ \ \Rightarrow\ \ x\ =\ \ldots\quad$ Note : no square formula required.

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2019-12-03 05:07:39
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