三次方程式の解の公式

ax³+bx²+cx+dの解の3つをx₁,x₂,x₃と表す

x₁=³√[-(27a²d+2b³-9abc/54a³)+√{(27a²d+2b³-9abc/54a³)²+(3ac-b²/9a²)³}]+³√[-(27a²d+2b³-9abc/54a³)-√{(27a²d+2b³-9abc/54a³)²+(3ac-b²/9a²)³}]-b/3a

x₂=(-1+√3i)/2
・³√[-(27a²d+2b³-9abc/54a³)+√{(27a²d+2b³-9abc/54a³)²+(3ac-b²/9a²)³}]+(-1-√3i)/2・³√[-(27a²d+2b³-9abc/54a³)-√{(27a²d+2b³-9abc/54a³)²+(3ac-b²/9a²)³}]-b/3a

x₃=(-1−√3i)/2
・³√[-(27a²d+2b³-9abc/54a³)+√{(27a²d+2b³-9abc/54a³)²+(3ac-b²/9a²)³}]+(-1+√3i)/2・³√[-(27a²d+2b³-9abc/54a³)-√{(27a²d+2b³-9abc/54a³)²+(3ac-b²/9a²)³}]-b/3a