Answer
$x=1/4, 2$
Work Step by Step
$\sqrt {9x-2}-2x =0$
$\sqrt {9x-2}-2x+2x =0+2x$
$\sqrt {9x-2}=2x$
$(\sqrt {9x-2})^2=(2x)^2$
$9x-2=4x^2$
$9x-2-9x+2=4x^2-9x+2$
$4x^2-9x+2=0$
$(4x-1)(x-2)=0$
$4x-1=0$
$4x-1+1=0+1$
$4x=1$
$4x/4=1/4$
$x=.25$
$x-2=0$
$x=2$
$\sqrt {9x-2}-2x =0$
$\sqrt {9*.25-2}-2*.25 =0$
$\sqrt{2.25-2}-.5=0$
$\sqrt {.25}-.5=0$
$\sqrt {1/4}-.5=0$
$\sqrt 1/\sqrt4 -.5=0$
$1/2 -.5=0$
$.5-.5=0$ (true)
$\sqrt {9x-2}-2x =0$
$\sqrt {9*2-2}-2*2 =0$
$\sqrt {18-2}-4 =0$
$\sqrt {16}-4 =0$
$4-4=0$ (true)
