<s>[INST] If $\frac{5x}{2x^2+5x+1}=\frac13$ then the value of $x+\frac{1}{2x}$ is If $\frac{5x}{2x^2+5x+1}=\frac13$ then the value of $x+\frac{1}{2x}$ is
note $5x=1$
$2x^2+5x+1=3$
or
$15x=2x^2+5x+1$
so $2x^2-10x+1$
so $\frac{5+\sqrt{23}}2$ or $\frac{5-\sqrt{23}}2$
 [/INST] HINT:
As $x\ne0,$
$$3=\frac{5x}{2x^2+5x+1}=\frac{5/2}{x+5/2+1/2x}$$
$$\iff\frac{x+5/2+1/2x}{5/2}=\frac13$$
Hope you can take it from here
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