Question
$$\frac{1730}{x} = \frac{1730}{2x}+\frac{7}{3}$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 7 }{ 5190 }-\dfrac{\sqrt{ 53872249 }}{ 5190 } & x_2 = -\dfrac{ 7 }{ 5190 }+\dfrac{\sqrt{ 53872249 }}{ 5190 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1730}{x} &= \frac{1730}{2x}+\frac{7}{3}&& \text{multiply ALL terms by } \color{blue}{ x\cdot2\cdot3 }. \\[1 em]x\cdot2\cdot3\cdot\frac{1730}{x} &= x\cdot2\cdot3\cdot\frac{1730}{2x}+x\cdot2\cdot3\cdot\frac{7}{3}&& \text{cancel out the denominators} \\[1 em]10380 &= 5190x^2+14x&& \text{move all terms to the left hand side } \\[1 em]10380-5190x^2-14x &= 0&& \text{simplify left side} \\[1 em]-5190x^2-14x+10380 &= 0&& \\[1 em] \end{aligned} $$
$ -5190x^{2}-14x+10380 = 0 $ is a quadratic equation.
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