$\frac{10x + 3}{12} = 1 + \frac{6 + 8x}{9}$
$\Leftrightarrow \frac{10x + 3}{12} = \frac{6 + 8x + 9}{9}$
$\Leftrightarrow \frac{10x + 3}{12} = \frac{8x + 15}{9}$
$\Leftrightarrow (10x + 3).9 = (8x + 15).12$
$\Leftrightarrow 90x + 27 = 96x + 180$
$\Leftrightarrow 6x = -153$
$\Leftrightarrow x = -\frac{51}{2}$