[tex] 8x^2=2x+1\ \ \ \ |-2x-1\\\\8x^2-2x-1=0\\\\8x^2+2x-4x-1=0\\\\2x(4x+1)-1(4x+1)=0\\\\(4x+1)(2x-1)=0\iff4x+1=0\ \vee\ 2x-1=0\\\\4x+1=0\ \ \ |-1\\4x=-1\ \ \ |:4\\x=-0.25\\\\2x-1=0\ \ \ |+1\\2x=1\ \ \ \ |:2\\x=0.5\\\\Answer:\ x=-0.25\ or\ x=0.5 [/tex]
