Parabola exercise and checking a log-equation

The parabola exercise is this one:

'A parabola is given by the equation y = ax^2 + ax + 1, where a is a positive real number different from zero.

(a): Determine a so that the parabola has exactly one intersection point with the x-axis.

(b): At the point P(x0,y0) the parabola has a tangent which is parallel to the line with the equation y = 8x - 800. Find the value of X0'

And then I had this log equation, and if someone would check if it's right, that'd make me very happy. (:

$\displaystyle

\log_5 (2x+7) - 3 = \log_5 x

$

$\displaystyle

\log_5 (2x+7) - \log_5 125 = \log_5 x

$

$\displaystyle

\log_5 ((2x+7)/125) = \log_5 x

$

$\displaystyle

(2x+7)/125 = x

$

$\displaystyle

2x+7 = 125x

$

$\displaystyle

x = 118

$