Answer
$x = \frac{-7+\sqrt {2793}}{4}$
Work Step by Step
$\log_7 x + \log_7 (2x+7) -3 = 0$
$\log_7 x(2x+7)- 3 = 0$
$\log_7 x(2x+7)= 3$
$7^{3} = x(2x+7)$
$343 = 2x^{2} + 7x$
$2x^{2} + 7x - 343 = 0$
$x = \frac{-(7)±\sqrt {7^{2}-4(2)(-343)}}{2(2)}$
$x = \frac{-7±\sqrt {49+2744}}{2(2)}$
$x = \frac{-7±\sqrt {49+2744}}{4}$
$x = \frac{-7±\sqrt {2793}}{4}$
$x = \frac{-7+\sqrt {2793}}{4}$