Answer
$x= (-2+\sqrt 5)/2, (-2-\sqrt 5)/2$
Work Step by Step
$4x^2+8x-1=0$
$4x^2+8x-1+1=0+1$
$4x^2+8x=1$
$4(x^2+2x)=1$
$4(x^2+2x+(2/2)^2)=1+4*(2/2)^2$
$4(x^2+2x+1^2)=1+4*(1^2)$
$4(x^2+2x+1)=1+4*1$
$4(x+1)^2=1+4$
$4(x+1)^2=5$
$4(x+1)^2/4=5/4$
$(x+1)^2=5/4$
$\sqrt {(x+1)^2} =\sqrt {5/4}$
$x+1 = \sqrt 5 /±2$
$x+1-1 = -1+\sqrt 5 /±2$
$x= (-2+\sqrt 5)/2, (-2-\sqrt 5)/2$
