$$x\cdot4+3x\cdot3-39x\cdot2-83x-42 = \frac{1}{x}+7$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 49 }{ 296 }-\dfrac{ 3 \sqrt{ 201}}{ 296 } & x_2 = -\dfrac{ 49 }{ 296 }+\dfrac{ 3 \sqrt{ 201}}{ 296 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x\cdot4+3x\cdot3-39x\cdot2-83x-42 &= \frac{1}{x}+7&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]xx\cdot4+x3x\cdot3-x39x\cdot2-x\cdot83x-x\cdot42 &= x\cdot\frac{1}{x}+x\cdot7&& \text{cancel out the denominators} \\[1 em]4x^2+9x^2-78x^2-83x^2-42x &= 1+7x&& \text{simplify left and right hand side} \\[1 em]-148x^2-42x &= 7x+1&& \text{move all terms to the left hand side } \\[1 em]-148x^2-42x-7x-1 &= 0&& \text{simplify left side} \\[1 em]-148x^2-49x-1 &= 0&& \\[1 em] \end{aligned} $$
$ -148x^{2}-49x-1 = 0 $ is a quadratic equation.
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