Answer
$x=-4$
Work Step by Step
Using the properties of equality, the given equation, $
x-\sqrt{4-3x}=-8
,$ is equivalent to
\begin{array}{l}\require{cancel}
x+8=\sqrt{4-3x}
.\end{array}
Squaring both sides of the equation above, then the solution/s is/are
\begin{array}{l}\require{cancel}
(x)^2+2(x)(8)+(8)^2=4-3x
\\\\
x^2+16x+64=4-3x
\\\\
x^2+(16x+3x)+(64-4)=0
\\\\
x^2+19x+60=0
\\\\
(x+15)(x+4)=0
\\\\
x=\{ -15,-4 \}
.\end{array}
Upon checking, only $
x=-4
$ satisfies the original equation.