Solve a cubic polynomial for x, given coefficients a, b, c, d in standard form = ax^3 - bx^2 + cx - d = 0. Uses homegrown cubic root function sqrt3() because Xquery's math library cannot raise a negative number to a decimal power. http://www.math.vanderbilt.edu/~schectex/courses/cubic/

solveCubicEquation

declare function local:solveCubicEquation($a as xs:double, $b as xs:double, $c as xs:double, $d as xs:double) {
  let $big := ((-math:pow($b,3.0)) div (27.0 * math:pow($a,3.0))) + (($b * $c) div (6.0 * math:pow($a,2.0))) - ($d div (2.0 * $a))
  let $small := ($c div (3.0 * $a)) - (math:pow($b,2.0) div (9.0 * math:pow($a,2.0)))
  let $tail := ($b div (3.0 * $a))
  let $x := math:pow($big + math:sqrt(math:pow($big,2.0) + math:pow($small,3.0)), (1.0 div 3.0)) + local:sqrt3( $big - math:sqrt(math:pow($big,2.0) + math:pow($small,3.0)) ) - $tail 
  return $x
};