\(7x^2+14x-21=0\)
=>\(x_1+x_2=-\dfrac{b}{a}=-\dfrac{14}{7}=-2;x_1x_2=-\dfrac{21}{7}=-3\)
\(A=\dfrac{x_2+3}{x_1}+\dfrac{x_1+3}{x_2}\)
\(=\dfrac{x_2^2+3x_2+x_1^2+3x_1}{x_1x_2}=\dfrac{\left(x_1+x_2\right)^2-2x_1x_2+3\left(x_1+x_2\right)}{x_1x_2}\)
\(=\dfrac{\left(-2\right)^2-2\cdot\left(-3\right)+3\cdot\left(-2\right)}{-3}=\dfrac{4+6-6}{-3}=-\dfrac{4}{3}\)