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.