Answer
$x=2$, $x=6$
Work Step by Step
$\sqrt {x-2} = \sqrt {4x+1} -3$
$(\sqrt {x-2})^2 = (\sqrt {4x+1} -3)^2$
$x-2 = (\sqrt {4x+1} -3)(\sqrt {4x+1} -3)$
$x-2= \sqrt {4x+1}*\sqrt{4x+1}+\sqrt {4x+1}*-3+\sqrt {4x+1}*-3=(-3)(-3)$
$x-2=4x+1-6\sqrt {4x+1}+9$
$x-2=4x+10-6\sqrt {4x+1}$
$x-2-4x-10=4x+10-6\sqrt {4x+1}-4x-10$
$-3x-12=-6\sqrt {4x+1}$
$(-3x-12)/-6=-6\sqrt {4x+1}/-6$
$.5x+2=\sqrt {4x+1}$
$(.5x+2)^2=(\sqrt {4x+1})^2$
$(.5x+2)^2=(4x+1)$
$(.5x+2)(.5x+2)=(4x+1)$
$.5x*.5x+2*.5x+2*.5x+2*2=4x+1$
$.25x^2+x+x+4=4x+1$
$.25x^2+2x+4=4x+1$
$.25x^2+2x+4-4x-1=4x+1-4x-1$
$.25x^2-2x+3=0$
$a=.25$, $b=-2$, $c=3$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-(-2)±\sqrt {(-2)^2-4*.25*3})/2*.25$
$x=(2±\sqrt {4-3})/.5$
$x=(2±\sqrt {1})/.5$
$x=(2±1)/.5$
$x=(2+1)/.5$
$x=3/.5$
$x=6$
$x=(2-1)/.5$
$x=1/.5$
$x=2$
