$3x-2\sqrt{ 3x \times \left( x+4 \right) }+x+4=4$
Cancel equal terms on both sides of the equation$3x-2\sqrt{ 3x \times \left( x+4 \right) }+x=0$
Distribute $3x$ through the parentheses$3x-2\sqrt{ 3{x}^{2}+12x }+x=0$
Collect like terms$4x-2\sqrt{ 3{x}^{2}+12x }=0$
Move the variable to the right-hand side and change its sign$-2\sqrt{ 3{x}^{2}+12x }=-4x$
Divide both sides of the equation by $-2$$\sqrt{ 3{x}^{2}+12x }=2x$
Square both sides of the equation$3{x}^{2}+12x=4{x}^{2}$
Move the variable to the left-hand side and change its sign$3{x}^{2}+12x-4{x}^{2}=0$
Collect like terms$-{x}^{2}+12x=0$
Factor out $-x$ from the expression$-x \times \left( x-12 \right)=0$
Change the signs on both sides of the equation$x \times \left( x-12 \right)=0$
When the product of factors equals $0$, at least one factor is $0$$\begin{array} { l }x=0,\\x-12=0\end{array}$
Solve the equation for $x$$\begin{array} { l }x=0,\\x=12\end{array}$
Check if the given value is the solution of the equation$\begin{array} { l }\sqrt{ 3 \times 0 }-\sqrt{ 0+4 }=2,\\x=12\end{array}$
Check if the given value is the solution of the equation$\begin{array} { l }\sqrt{ 3 \times 0 }-\sqrt{ 0+4 }=2,\\\sqrt{ 3 \times 12 }-\sqrt{ 12+4 }=2\end{array}$
Simplify the expression$\begin{array} { l }-2=2,\\\sqrt{ 3 \times 12 }-\sqrt{ 12+4 }=2\end{array}$
Simplify the expression$\begin{array} { l }-2=2,\\2=2\end{array}$
The equality is false, therefore $x=0$ is not a solution of the equation$\begin{array} { l }x≠0,\\2=2\end{array}$
The equality is true, therefore $x=12$ is a solution of the equation$\begin{array} { l }x≠0,\\x=12\end{array}$
The equation has one solution$x=12$