\[\begin{array}{l}
x\left( {5{x^3} + 2} \right) - 2\left( {\sqrt {2x + 1} - 1} \right) = 0\,\,\,\left( * \right)\\
DK:\,\,\,x \ge - \frac{1}{2}.\\
\left( * \right) \Leftrightarrow 5{x^4} + 2x - 2\sqrt {2x + 1} + 2 = 0\\
\Leftrightarrow 2x + 1 - 2\sqrt {2x + 1} + 1 + 5{x^4} = 0\\
\Leftrightarrow {\left( {\sqrt {2x + 1} - 1} \right)^2} + 5{x^4} = 0\\
\Leftrightarrow \left\{ \begin{array}{l}
\sqrt {2x + 1} - 1 = 0\\
{x^4} = 0
\end{array} \right.\,\,\,\left( {do\,\,\,\left\{ \begin{array}{l}
{\left( {\sqrt {2x + 1} - 1} \right)^2} \ge 0\,\,\forall x \ge - \frac{1}{2}\\
{x^4} \ge 0\,\,\forall x
\end{array} \right.} \right)\\
\Leftrightarrow \left\{ \begin{array}{l}
\sqrt {2x + 1} = 1\\
x = 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
2x + 1 = 1\\
x = 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = 0\\
x = 0
\end{array} \right. \Leftrightarrow x = 0\,\,\,\left( {tm} \right).\\
Vay\,\,\,pt\,\,co\,\,nghiem\,\,x = 0.
\end{array}\]
