3. Among the following statements about the roots of the equation $\sqrt{4 x^{2}+2 x+1}-\sqrt{4 x^{2}+14 x+5}=6 x+2$, the correct one is
A. The equation has no negative real roots
B. The equation has no rational roots
C. The equation has two real roots
D. The equation has only one real root
Solve:
$$
\sqrt{4 x^{2}+2 x+1}-\sqrt{4 x^{2}+14 x+5}=\frac{-12 x-4}{\sqrt{4 x^{2}+2 x+1}+\sqrt{4 x^{2}+14 x+5}}=6 x+2,
$$

Obviously, $6 x+2=0 \Rightarrow x=-\frac{1}{3}$ is a root of the original equation;
If $6 x+2 \neq 0$, then $\sqrt{4 x^{2}+2 x+1}+\sqrt{4 x^{2}+14 x+5}=-2$, which is a contradiction.
Therefore, the original equation has only one real root, so the answer is $D$.