$$-\frac{1}{500}d^2+\frac{18}{25}d+4 = 0$$
Answer
$$ \begin{matrix}d_1 = 180-20 \sqrt{ 86 } & d_2 = 180+20 \sqrt{ 86 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} -\frac{1}{500}d^2+\frac{18}{25}d+4 &= 0&& \text{multiply ALL terms by } \color{blue}{ 500 }. \\[1 em]-500 \cdot \frac{1}{500}d^2+500\frac{18}{25}d+500\cdot4 &= 500\cdot0&& \text{cancel out the denominators} \\[1 em]-d^2+360d+2000 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+360x+2000 = 0 $ is a quadratic equation.
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