$$\frac{ x-(7-8x) }{ 9x-(3+4x) } = \frac{ 2 }{ 3 }$$
$x=\frac{15}{17}\approx 0.882352941$
$$3\left(x-\left(7-8x\right)\right)=2\left(5x-3\right)$$
$$3\left(x-7+8x\right)=2\left(5x-3\right)$$
$$3\left(9x-7\right)=2\left(5x-3\right)$$
$$27x-21=2\left(5x-3\right)$$
$$27x-21=10x-6$$
$$27x-21-10x=-6$$
$$17x-21=-6$$
$$17x=-6+21$$
$$17x=15$$
$$x=\frac{15}{17}$$
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