[tex]\displaystyle\bf\\\Big(x^{2} -x+4\Big)^{2}-10\Big(x^{2} -x+4\Big)+16=0\\\\x^{2} -x+4=m\\\\m^{2} -10m+16=0\\\\D=(-10)^{2} -4\cdot 16=100-64=36=6^{2} \\\\\\m_{1} =\frac{10-6}{2}=2\\\\\\m_{2} =\frac{10+6}{2} =8\\\\\\1)\\\\x^{2} -x+4=2\\\\x^{2} -x+2=0\\\\D=(-1)^{2}-4\cdot2=1-8=-7 < 0\\\\x\in \oslash\\\\2)\\\\x^{2} -x+4=8\\\\x^{2} -x-4=0\\\\D=(-1)^{2} -4\cdot(-4)=1+16=17\\\\\\x_{1} =\frac{1-\sqrt{17} }{2}\\\\\\x_{2} =\frac{1+\sqrt{17} }{2}[/tex]

[tex]\displaystyle\bf\\Otvet \ : \ \frac{1-\sqrt{17} }{2} \ \ ; \ \ \frac{1+\sqrt{17} }{2}[/tex]