Answer
$x=4$
Work Step by Step
$x-\sqrt {13-3x}-3=0$
$x-3 = \sqrt {13-3x}$
$(x-3)^2 = (\sqrt {13-3x})^2$
$x*x+x(-3)+x(-3)+(-3)(-3) = 13-3x$
$x^2-6x+9=13-3x$
$x^2-3x-4=0$
$(x-4)(x+1)=0$
$x-4=0$
$x=4$
$x+1=0$
$x=-1$
$x=4$
$x-\sqrt {13-3x}-3=0$
$4-\sqrt {13-3*4}-3=0$
$4-\sqrt {13-12}-3=0$
$1-\sqrt 1=0$
$1-1=0$ (true)
$x=-1$
$x-\sqrt {13-3x}-3=0$
$-1-\sqrt {13-3(-1)}-3=0$
$-1-\sqrt{13+3}-3=0$
$-1-\sqrt {16}=3$
$-1-4=3$
$-5=3$ (false)
