some of you must be having the idea that cubic equations roots cant be found out.but in fact they can be found out

the standard form is y^3+3a*y^2+3by+c=0

put y=x-a the equation reduces to of the form x^3-3px+q=0----1

to solve the equation put x=z/n

and we have z^3-3*p*n^2*z+q*n^3=0

(cos a)^3-(3/4cos a)-1/4*cos 3a=0-----2

each of u would surely acquainted with that

now compare 1 and 2 u will arrive at n=  (1/4p)^1/2

then cos 3a= - 4q((1/4p)^3/2)-----3

the equation 3 can always be solved if 4q((1/4p)^3/2)<1

i.e q^2<4*p^3

if a be the smallest angle satisfying the equation 3

then also the values a+120 and a+240

so that the roots are (cos a)/n,(cos(a+120))/n and (cos(a+240))/n

and then u may get all the roots and convert it into the original form.

HOPE THIS IS HELPFUL TO ALL MATHS LOVERS