+486 First, simplifying the right side gives $\frac{4x^2+5x+8x^2}{2x}=\frac{12x^2+5x}{2x}=\frac{12x+5}{2}$
Then, multiplying by $2(x+4)$ to get rid of fractions gives $2(3x+12)=(12x+5)(x+4)$.
Moving everything to one side gives $(12x+5)(x+4)-(6x+24)=0$.
Expanding everything gives $12x^2+53x+20-6x-24=0$.
Simplifying gives $12x^2+47x-4=0$.
Factoring this equation gives $(x-\frac{1}{12})(x+4)=0$.
So, our two solutions are $\frac{1}{12}$ and $-4$.
But wait!
$-4$ is extraneous, because plugging it in causes division by 0! That means $\boxed{x=\frac{1}{12}}$ is the only solution
