$$7(2x-3)=4 \sqrt{ 7 } (-9+6x)$$
$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$
$$14x-21=4\sqrt{7}\left(-9+6x\right)$$
$$14x-21=-36\sqrt{7}+24\sqrt{7}x$$
$$14x-21-24\sqrt{7}x=-36\sqrt{7}$$
$$14x-24\sqrt{7}x=-36\sqrt{7}+21$$
$$\left(14-24\sqrt{7}\right)x=-36\sqrt{7}+21$$
$$\left(14-24\sqrt{7}\right)x=21-36\sqrt{7}$$
$$\frac{\left(14-24\sqrt{7}\right)x}{14-24\sqrt{7}}=\frac{21-36\sqrt{7}}{14-24\sqrt{7}}$$
$$x=\frac{21-36\sqrt{7}}{14-24\sqrt{7}}$$
$$x=\frac{3}{2}$$
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