Question Number 114388 by ajfour last updated on 18/Sep/20

Developed the formula for the cubic  equation when it has three real roots  and Cardano is just not suitable as  discriminant gets negative..     Given    x^3 −bx−c=0    with  b>0 , c>0   (t/b)=1+((15)/2)((c^2 /b^3 ))+(√(((c^2 /b^3 ))[49−((75)/4)((c^2 /b^3 ))]))       x=(√(t+((4c^2 )/b^2 ))) −((3c)/b)  ★  mrW Sir, MjS Sir  please check!

Commented byMJS_new last updated on 18/Sep/20

it′s not exact  x^3 −((244)/3)x−((1456)/(27))=0 ⇒ x∈{−((26)/3), −(2/3), ((28)/3)}  but your formula gives  x≈9.33355157 instead of 9.3^•

Commented byajfour last updated on 18/Sep/20

yes sir, i found the error! thanks.