Question
$$4x-5+\frac{6}{x}-5 = 0$$
Answer
$$ \begin{matrix}x_1 = 1 & x_2 = \dfrac{ 3 }{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 4x-5+\frac{6}{x}-5 &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot4x-x\cdot5+x\cdot\frac{6}{x}-x\cdot5 &= x\cdot0&& \text{cancel out the denominators} \\[1 em]4x^2-5x+6-5x &= 0&& \text{simplify left side} \\[1 em]4x^2-10x+6 &= 0&& \\[1 em] \end{aligned} $$
$ 4x^{2}-10x+6 = 0 $ is a quadratic equation.
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