Cardano solves x^3 +6x=20

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Choose u and v so that
u^3 - v^3 = 20 and 
u v = 2

Let x = u - v

u^3 - v^3 = 20 = x^3 + 3xv^2 + 3vx^2
x^3 = u^3 - 3vu^2 + 3uv^2 - v^3
so 3vu^2 - 3uv^2 = 3xv^2 + 3vx^2 = 3xv(v+x) = 3xvu = 6x
Thus  x^3 +6x = u^3 - v^3 = 20