input engineering calculation with verification

Below is an example {calc} of a short engineering calculation.
I want to insert this as a standard calculation input{calc} in a main document.
Sometimes I want to use this multiple times in the main document with different values (t, s, p, etc.).

I made something myself with luacode and marginnote.
But the marginnote does not do what I want. Because when input{calc} in the main document the "marginparwidth" needs to be adjusted temporarily.

Is there someone who can help me with a solid concept for this short engineering calculation?
Many thanks in advance!

documentclass[12pt,a4paper]{article}
usepackage[fleqn]{amsmath}
usepackage{luacode}
usepackage{tabularx}
usepackage{marginnote}
usepackage[left=1.3cm,right=4.6cm,top=1.8cm,bottom=4.0cm,marginparwidth=3.4cm]{geometry}
usepackage{scrextend}

newenvironment{conditions*}
  {parvspace{abovedisplayskip}noindent
   tabularx{columnwidth}{>{$}l<{$} @{${}={}$} >{raggedrightarraybackslash}X|}}
  {endtabularxparvspace{belowdisplayskip}}

begin{luacode}
    t  = 3
    s  = 454
    p  = 4.51
    k  = 0.00394
    w  = 7.04
    a  = 1.5
end{luacode}

begin{luacode*}
    sqrt = math.sqrt

    treq = function (t, s, p, k, w, a) 
            return k *s * sqrt(p / w) + a 
    end

    print = function (d,s) 
        if d == 0 then
         format = "%d"
        else
         format = "%." .. d .. "f"
        end
        tex.sprint(string.format(format,s));
    end
end{luacode*}

defluaprint#1{directlua{tex.print(#1)}}
newcommand{lp}[2][16]{directlua{print(#1,#2)}}

begin{document}
The plating t is to be not less in thickness than that obtained from the following equation:
begin{equation*}
tag{formule 11.1}
begin{split}
t_{req} & = k times  s times sqrt{frac{p}{k}}+{a} 
        & = luaprint{k} times  luaprint{s} times sqrt{frac{luaprint{p}}{luaprint{k}}}+{luaprint{a}} 
        & = lp[2]{treq(luaprint{t}, luaprint{s}, luaprint{p}, luaprint{k}, luaprint{w}, luaprint{a})}
        marginnote{$t=luaprint{w}mathrm{mm}$}
end{split}
end{equation*}

where:
begin{conditions*}
t       &   marginnote{$t=luaprint{t}mathrm{mm}$}
            chosen thickness 
t_{req} &   required thickness 
s       &   marginnote{$s=luaprint{s}mathrm{mm}$}
            spacing of stiffeners 
p       &   marginnote{$p=luaprint{p}mathrm{kN.m^{-2}}$}
            minimum deck loading 
k       &   marginnote{$k=luaprint{k}mathrm{}$}
            factor 
w       &   marginnote{$w=luaprint{w}mathrm{kN.m^{-2}}$}
            reference loading 
a       &   marginnote{$a=luaprint{a}mathrm{}$}
            corrosion allowance 
end{conditions*}
end{document}