\[\sqrt{x^{2} + 2x + 5} = \sqrt{5x + 15}\]
\[ОДЗ:\]
\[1)\ x^{2} + 2x + 5 \geq 0\]
\[D_{1} = 1 - 5 < 0\]
\[x - любое\ число.\]
\[2)\ 5x + 15 \geq 0\]
\[5x \geq - 15\]
\[x \geq - 3.\]
\[x^{2} + 2x + 5 = 5x + 15\]
\[x^{2} - 3x - 10 = 0\]
\[x_{1} + x_{2} = 3;\ \ x_{1} \cdot x_{2} = - 10\]
\[x_{1} = - 2;\ \ \ x_{2} = 5.\]
\[Оба\ корня\ подходят,\ найдем\ сумму:\]
\[x_{1} + x_{2} = 3.\]
\[Ответ:3.\]