Question
$$144 = 16+\frac{64}{x}-x$$
Answer
$$ \begin{matrix}x_1 = -64-8 \sqrt{ 65 } & x_2 = -64+8 \sqrt{ 65 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 144 &= 16+\frac{64}{x}-x&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot144 &= x\cdot16+x\cdot\frac{64}{x}-xx&& \text{cancel out the denominators} \\[1 em]144x &= 16x+64-x^2&& \text{simplify right side} \\[1 em]144x &= -x^2+16x+64&& \text{move all terms to the left hand side } \\[1 em]144x+x^2-16x-64 &= 0&& \text{simplify left side} \\[1 em]x^2+128x-64 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}+128x-64 = 0 $ is a quadratic equation.
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