$$(x-3/5)+(x-4/9)=6-(2x-1/45)$$
$x = \frac{53}{30} = 1\frac{23}{30} \approx 1.766666667$
$$2x-\frac{3}{5}-\frac{4}{9}=6-\left(2x-\frac{1}{45}\right)$$
$$2x-\frac{27}{45}-\frac{20}{45}=6-\left(2x-\frac{1}{45}\right)$$
$$2x+\frac{-27-20}{45}=6-\left(2x-\frac{1}{45}\right)$$
$$2x-\frac{47}{45}=6-\left(2x-\frac{1}{45}\right)$$
$$2x-\frac{47}{45}=6-2x-\left(-\frac{1}{45}\right)$$
$$2x-\frac{47}{45}=6-2x+\frac{1}{45}$$
$$2x-\frac{47}{45}=\frac{270}{45}-2x+\frac{1}{45}$$
$$2x-\frac{47}{45}=\frac{270+1}{45}-2x$$
$$2x-\frac{47}{45}=\frac{271}{45}-2x$$
$$2x-\frac{47}{45}+2x=\frac{271}{45}$$
$$4x-\frac{47}{45}=\frac{271}{45}$$
$$4x=\frac{271}{45}+\frac{47}{45}$$
$$4x=\frac{271+47}{45}$$
$$4x=\frac{318}{45}$$
$$4x=\frac{106}{15}$$
$$x=\frac{\frac{106}{15}}{4}$$
$$x=\frac{106}{15\times 4}$$
$$x=\frac{106}{60}$$
$$x=\frac{53}{30}$$
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