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 $\{4,6\}$.
@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!
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.