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$4 \alpha^3 + 27 \beta^2 \geq 0$:
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The solution of Equation~\ref{eq:simple-cubic-equation-for-quadratic-distance}
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One solution of Equation~\ref{eq:simple-cubic-equation-for-quadratic-distance}
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is
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\[x = \frac{t}{\sqrt[3]{18}} - \frac{\sqrt[3]{\frac{2}{3}} \alpha }{t}\]
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