Can anyone solve this task?

d=0 is correct.

The coefficients a,b and c must be determined after the desired function has to be third degree.

(1) f(8)=64 with d=0

At f'(x)=0, only the positive solution comes into question:

(2)8=(sqrt(b^2-3ac)-b)/3a

(3)64=f(sqrt(b^2-3ac)-b)/3a)

Solutions:

a=z × 1

b = 16z-1

c=64z+16

For example, you can choose 1

f(x)=x^3=17x^2+80x