To apply the Cardano method it is necessary to bring this equation to an canonical form:
y^3+py+q=0
write down our cubic equation in the general form
ax^3+bx^2+cx+d=0
1*x^3+1*x^2+0*x+0=0
We will replace the variable
x=y-(b/3a)
by changing the variable can be reduced to the above canonical form with coefficients
p=c/a-(b^2/3a^2)=-1/3
q= (2b^3/27a^3)-(bc/3a^2)+d/a=2/27
the canonical form will have this form
y^3-1/3y+2/27=0
Determine the value
Q=(p/3)^3+(q/2)^2=-1/729+1/729=0
Q = 0 is a single real real root
y=a+b
where
a=((-q/2)+Q^½)^⅓
b=((-q/2)-Q^½)^⅓
y=(-1/3)+(-1/3)=-2/3
then
x= (-2/3)-(1/3)=-1
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