For the general quadratic equation:
color(white)("XXX")color(red)(a)x^2+color(blue)(b)x+color(green)(c)=0
the quadratic formula tells us that
color(white)("XXX")x=(-color(blue)(b)+-sqrt(color(blue)(b)^2-4color(red)(a)color(green)(c)))/(2(color(red)(a)))
The given equation: x^2-4x-1=0 can be written explicitly in the general form as:
color(white)("XXX")x=color(red)(1)x^2+color(blue)(""(-4))+color(green)(""(-1))=0
So the solution is
color(white)("XXX")x=(-color(blue)(""(-4))+-sqrt(color(blue)(""(-4))^2-4color(red)(""(1))color(green)(""(-1))))/(2(color(red)(1))
color(white)("XXXX")=(4+-sqrt(20))/2
color(white)("XXXX")=2+-sqrt(5)
