Correct. The area of the flag is $\displaystyle{20}\cdot{12}={240}\usepackage{cmbright}\Huge\$ . Adding a border of width x, the new area of the flag is $\displaystyle{\left({20}+{2}{x}\right)}{\left({12}+{2}{x}\right)}\usepackage{cmbright}\Huge\$ . The area of the border is given by $\displaystyle{\left({20}+{2}{x}\right)}{\left({12}+{2}{x}\right)}-{\left({20}\right)}{\left({12}\right)}={228}\usepackage{cmbright}\Huge\$ , which simplifies to $\displaystyle{4}{{x}}^{{2}}+{64}{x}-{228}={0}\usepackage{cmbright}\Huge\$ .