a^3 + b^2 + c*x + d = 0, x = sqrt^3{ ( -{b^3}/{27*a^3 +{b*c}/{6*a^3} -d/{2*a} ) - sqrt^2{ ( -{b^3}/{27*a^3} +{b*c}/{6*a^3} -d/{2*a} )^2 + ( c/{3*a} - b^2/{9*a^2) )^3 } } + sqrt^3{ ( -{b^3}/{27*a^3 +{b*c}/{6*a^3} -d/{2*a} ) + sqrt^2{ ( -{b^3}/{27*a^3} +{b*c}/{6*a^3} -d/{2*a} )^2 + ( c/{3*a} - b^2/{9*a^2) )^3 } } - b/{3*a}
ax³ + bx² + cx + d = 0, __________________________________________________________________ | _______________________________________ | b³ bc d | b³ bc d c b² x = 3| ( - ---- + --- - -- ) - | ( - ---- + --- - -- )² + ( -- - --- )³ \| 27a³ 6a³ 2a \| 27a³ 6a³ 2a 3a 9a² __________________________________________________________________ | _______________________________________ | b³ bc d | b³ bc d c b² + 3| ( - ---- + --- - -- ) + | ( - ---- + --- - -- )² + ( -- - --- )³ \| 27a³ 6a³ 2a \| 27a³ 6a³ 2a 3a 9a² b - -- 3a