Correct. The area of the grass is: $\displaystyle{\left({36}-{2}{x}\right)}{\left({24}-{2}{x}\right)}={540}\usepackage{cmbright}\Huge\$

Multiply out: $\displaystyle{864}-{120}{x}+{4}{{x}}^{{2}}={540}\usepackage{cmbright}\Huge\$ , so $\displaystyle{324}-{120}{x}+{4}{{x}}^{{2}}={0}\usepackage{cmbright}\Huge\$

Divide by 4 and rearrange terms: $\displaystyle{{x}}^{{2}}-{30}{x}+{81}={0}\usepackage{cmbright}\Huge\$

Use the Quadratic Formula: $\displaystyle{x}=\frac{{-{\left(-{30}\right)}\pm\sqrt{{{{\left(-{30}\right)}}^{{2}}-{4}\cdot{1}\cdot{81}}}}}{{{2}\cdot{1}}}=\frac{{{30}\pm\sqrt{{576}}}}{{2}}\usepackage{cmbright}\Huge\$

So $\displaystyle{x}=\frac{{{30}\pm{24}}}{{2}}={27}\usepackage{cmbright}\Huge\$ or 3. The larger solution is impossible, so $\displaystyle{x}={3}\usepackage{cmbright}\Huge\$ feet.