<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] Here are the steps
$$
\frac{5x}{2x^{2}+5x+1}=\frac{1}{3}
$$
$$
15x=2x^{2}+5x+1
$$
$$
10x=2x^{2}+1
$$
What would we get if we divide both sides of the last equation by $2x$?
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