Solving cubic equations

[Clonk]

Using Julia and Polynomials.jl 
(<https://juliamath.github.io/Polynomials.jl/stable/>) with Nimjl 
<https://github.com/clonkk/nimjl>) - I used this method in the past for 
Polynomial of any order
    
    
    import nimjl
    Julia.init(1):
      Pkg:
        add("Polynomials")
    
    jlUseModule("Polynomials")
    var p = Julia.Polynomial([1, 12, -4, 8])
    echo p
    #1 + 12*x - 4*x^2 + 8*x^3
    var s = Julia.roots(p)
    echo s
    # ComplexF64[-0.08080510243721191 + 0.0im, 0.29040255121860614 - 
1.2093793342224015im, 0.29040255121860614 + 1.2093793342224015im]
    
    
    Run

Using a raw Nim you probably want to start at : 
<https://github.com/SciNim/polynumeric> but it's more experimental.
    
    
    import polynumeric
    
    var p = Poly(cofs: @[8'f32, -4, 12, 1])
    var s = p.roots()
    echo s
    
    
    Run

That said for finding read roots of a cubic polynomial it does the job. If you 
need more advanced functionality, feel free to open a PR. Like @xigoi said, the 
formulas aren't that complicated.