(x+8)(x+2)=279

$$\boxed{(x+8)(x+2)=279}
\\
\hline
\begin{array}{rcl}
x^2+2x+8x+16&=&279\\
x^2+10x-279+16&=&0\\
x^2+10x-263&=&0
\end{array}
\hline$$

$$x_{1,2}=
\dfrac{
-10\pm\sqrt{10^2-4(-263)}
}
{2} \\\\
x_{1,2}=-5\pm\sqrt{25+263} \\
x_{1,2}=-5\pm\sqrt{288} \\
x_{1,2}=-5\pm\sqrt{144*2} \\
x_{1,2}=-5\pm12\sqrt{2} \\
}
\boxed{
x_1 = -5+12\sqrt{2} = 11.9705627485 \qquad x_2 = -5-12\sqrt{2} = -21.9705627485}$$

.

This can be solved in the Equations part of the calculator on the home page of this site.

$$\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{8}}\right){\mathtt{\,\times\,}}\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right) = {\mathtt{279}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{\left({\frac{{\mathtt{5}}}{{\mathtt{2}}}}\right)}{\mathtt{\,-\,}}{\mathtt{5}}\\
{\mathtt{x}} = {\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{\left({\frac{{\mathtt{5}}}{{\mathtt{2}}}}\right)}{\mathtt{\,-\,}}{\mathtt{5}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{21.970\: \!562\: \!748\: \!477\: \!140\: \!6}}\\
{\mathtt{x}} = {\mathtt{11.970\: \!562\: \!748\: \!477\: \!140\: \!6}}\\
\end{array} \right\}$$