$
\eqalign{
& \frac{1}
{{\sqrt 3 }} = \frac{{8 - x}}
{x} \cr
& x = \sqrt 3 \left( {8 - x} \right) \cr
& x^2 = 3\left( {8 - x} \right)^2 \cr
& x^2 = 3\left( {64 - 16x + x^2 } \right) \cr
& x^2 = 192 - 48x + 3x^2 \cr
& 2x^2 - 48x + 192 = 0 \cr
& x^2 - 24x + 96 = 0 \cr
& (x - 12)^2 - 48 = 0 \cr
& x = 12 - 4\sqrt 3 \vee x = 12 + 4\sqrt 3 \,\,(v.n.) \cr
& x = 12 - 4\sqrt 3 \cr
& O_{\Delta ABC} = \frac{1}
{2} \cdot 8\left( {12 - 4\sqrt 3 } \right) = 48 - 16\sqrt 3 \cr}
$