Binomial theorem question. Find the value of the constant $k$ $$\left[(k+x)\left(2-\frac{x}{2}\right)\right]^6$$
where the coefficient of $x^{2}$ is $84$.Find the value of the constant $k$.
I tried to expand the equation but got a equation of degree 6 for some reason.

We have $$\frac{1}{2^6}*(x+k)^6(x-4)^6\\(x+k)^6(x-4)^6=(P(x)+15x^2k^4+6xk^5+k^6)(Q(x)+15x^2*4^4-6x*4^5+4^6)\\15*4^4*k^6-36*4^5*k^5+4^6*15k^4$$ We have isolated the coefficient of $x^2$ so we have $$15*4k^6-36*4^2k^5+15*4^3k^4=84$$ hence
$$5k^6-48k^5+80k^4=7$$
This equation is irreducible and Wolfram gives $$\color{red}{k\approx 0.603231}$$
