Answer:
[tex]\large\boxed{x=\dfrac{15-\sqrt{221}}{2}\ or\ x=\dfrac{15+\sqrt{221}}{2}}[/tex]
Step-by-step explanation:
[tex]f(x)=5x\\\\g(x)=x^2-10x+1\\\\f(x)=g(x)\to5x=x^2-10x+1\qquad\text{subtract 5x from both sides}\\\\x^2-15x+1=0\\\\\text{Use the quadratic formula}:\\\\ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\a=1,\ b=-15,\ c=1\\\\b^2-4ac=(-15)^2-4(1)(1)=225-4=221\\\\x=\dfrac{-(-15)\pm\sqrt{221}}{2(1)}=\dfrac{15\pm\sqrt{221}}{2}[/tex]
