Answer
$x=\frac{1}{2} $
Work Step by Step
$\sqrt{4-6x}=2x$
Square the both sides $\Rightarrow(\sqrt{4-6x})^2=(2x)^2$
Expand $\Rightarrow4-6x=4x^2$
$\Rightarrow4x^2+6x-4=0$
Divide by $2$ $\Rightarrow2x^2+3x-2=0$
Use the quadratic formula, where $a=2, b=3$ and $c=-2$
$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(3)\pm\sqrt{(3)^2-4(2)(-2)}}{2(2)}$
$\Rightarrow x=\dfrac{-3\pm\sqrt{9+16}}{4}=\dfrac{-3\pm\sqrt{25}}{4}=\dfrac{-3\pm5}{4}$
$x=\dfrac{-3+5}{4}=\dfrac{2}{4}=\dfrac{1}{2}$
or $x=\dfrac{-3-5}{4}=\dfrac{-8}{4}=-2$
Check the answer:
$x=-2$
LHS $\sqrt{4-6(-2)}=\sqrt{4+12}=\sqrt{16}=4$
RHS $2(-2)=-4$
LHS $\ne$ RHS
$x=-2 \color{red}{reject}$
$x=\frac{1}{2}$
LHS $\sqrt{4-6(\frac{1}{2})}=\sqrt{4-3}=\sqrt{1}=1$
RHS $2(\frac{1}{2})=1$
LHS $=$ RHS
$x=\frac{1}{2} $
