(х-3)^4 + (x-6)^4=16 

[latex]x-3=a\\ x-6=a-3\\ \\ a^2+(a-3)^2=16\\ 2a^4-12a^3+54a^2-108a+65=0\\ (a^4-6a^3+9a^2)+a^4-6a^3+45a^2-108a+65=0\\ (2a^4-12a^3+18a)+36a^2-108a+65=0\\ 2(a^2-3a)^2+36(a^2-3a)+65=0\\ a^2-3a=t\\ \\ 2t^2+36t+65=0\\ D=36^2-4*2*65=\sqrt{776}\\ t_{1}=\frac{36+\sqrt{776}}{4}\\ t_{2}=\frac{36-\sqrt{776}}{4}\\ \\ a^2-3a=\frac{-36+\sqrt{776}}{4} \\ \\ a=\frac{3-/+\sqrt{2\sqrt{194}-27}}{2}\\ x-3=\frac{3-/+\sqrt{2\sqrt{194}-27}}{2}\\ x=\frac{3-/+\sqrt{2\sqrt{194}-27}}{2}+3[/latex]