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