$$\frac{5(x-4)}{4}-\frac{2(x-9)}{3}=\frac{3(x-5}{5}$$
$x=240$
$$15\times 5\left(x-4\right)-20\times 2\left(x-9\right)=12\times 3\left(x-5\right)$$
$$75\left(x-4\right)-20\times 2\left(x-9\right)=12\times 3\left(x-5\right)$$
$$75x-300-20\times 2\left(x-9\right)=12\times 3\left(x-5\right)$$
$$75x-300-40\left(x-9\right)=12\times 3\left(x-5\right)$$
$$75x-300-40x+360=12\times 3\left(x-5\right)$$
$$35x-300+360=12\times 3\left(x-5\right)$$
$$35x+60=12\times 3\left(x-5\right)$$
$$35x+60=36\left(x-5\right)$$
$$35x+60=36x-180$$
$$35x+60-36x=-180$$
$$-x+60=-180$$
$$-x=-180-60$$
$$-x=-240$$
$$x=240$$
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