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+% solution to ax^3 + bx^2 + cx + d = 0
+% https://math.vanderbilt.edu/schectex/courses/cubic/
+\begin{align*}
+% first term
+x &= \sqrt[3]{
+  % first term, first subterm
+  \left ( \frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a} \right ) +
+
+  \sqrt{
+    % first term, second subterm
+    \left ( \frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a} \right )^2 +
+
+    % first term, third subterm
+    \left ( \frac{c}{3a} - \frac{b^2}{9a^2} \right )^3
+  }
+} \\
+
+&+
+
+% second term
+\sqrt[3]{
+  % first term, second subterm
+  \left ( \frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a} \right ) -
+
+  \sqrt{
+    % second term, second subterm
+    \left ( \frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a} \right )^2 +
+
+    % second term, third subterm
+    \left ( \frac{c}{3a} - \frac{b^2}{9a^2} \right )^3
+  }
+} \\
+
+&-
+
+% third part
+\frac{b}{3a}
+\end{align*}