$$\frac{2x-3}{5}+\frac{x+3}{4}=\frac{4x+1}{7}$$
$x=-\frac{1}{11}\approx -0.090909091$
$$28\left(2x-3\right)+35\left(x+3\right)=20\left(4x+1\right)$$
$$56x-84+35\left(x+3\right)=20\left(4x+1\right)$$
$$56x-84+35x+105=20\left(4x+1\right)$$
$$91x-84+105=20\left(4x+1\right)$$
$$91x+21=20\left(4x+1\right)$$
$$91x+21=80x+20$$
$$91x+21-80x=20$$
$$11x+21=20$$
$$11x=20-21$$
$$11x=-1$$
$$x=\frac{-1}{11}$$
$$x=-\frac{1}{11}$$
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