<s>[INST] Having problems finding $x$ in terms of $a$ and $b$. I have attempted this question but have not found a solution. I am currently stuck. Hints on how I may go further would be helpful. Thank You in advance.
The Question:
$$\frac{a^2b}{x^2} + \left(1+\frac{b}{x}\right)a = 2b+ \frac{a^2}{x}$$
What I have done so far that I believe is correct:
$$\frac{a^2b}{x^2} + \frac{ab}{x} + a = 2b+ \frac{a^2}{x}$$
If you would like to see other work that I have attempted on this question I can also place it up. 
 [/INST] Take the equation:
$$\frac{a^2b}{x^2} + \frac{ab}{x} + a = 2b+ \frac{a^2}{x}$$
Multiply each side by $x^2$:
$$a^2b+abx+ax^2=2bx^2+a^2x$$
Subtract $2bx^2+a^2x$ from each side:
$$a^2b+abx+ax^2-2bx^2-a^2x=0$$
Rearrange it as a quadratic equation:
$$(a-2b)x^2+(ab-a^2)x+(a^2b)=0$$
And solve as you would any quadratic equation:
$$x_{1,2}=\frac{-(ab-a^2)\pm\sqrt{(ab-a^2)^2-4(a-2b)(a^2b)}}{2(a-2b)}$$
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