#### Answer

The solution of the given equation is $3$.

#### Work Step by Step

Square both sides to obtain:
$(2x)^2=(\sqrt{11x+3})^2
\\4x^2=11x+3
\\4x^2-11x-3=0$
Factor the trinomial:
$(4x+1)(x-3)=0$
Use the Zero Factor Property by equating each factor to zero, then solve each equation to obtain:
\begin{array}{ccc}
\\&4x+1=0 &\text{or} &x-3=0
\\&4x=-1 &\text{or} &x=3
\\&x=-\frac{1}{4} &\text{or} &x=3
\end{array}
Note that when $x=-\frac{1}{4}$: the left side of the given equation becomes $-\frac{1}{2}$.
Since the right side of the given equation involves a principal square root, its value must be non-negative.
Thus, $-\frac{1}{4}$ is not a solution of the equation.
Therefore, the solution of the given equation is $3$.