A trinomial in the form $\displaystyle{{r}}^{{2}}-{2}{r}{s}+{{s}}^{{2}}\usepackage{cmbright}\Huge\$ can be factored as $\displaystyle{{\left({r}-{s}\right)}}^{{2}}\usepackage{cmbright}\Huge\$ . So the left side is:

$\displaystyle{9}{{x}}^{{2}}-{30}{x}+{25}={{\left({3}{x}\right)}}^{{2}}-{2}{\left({3}{x}\right)}{\left({5}\right)}+{{5}}^{{2}}={{\left({3}{x}-{5}\right)}}^{{2}}\usepackage{cmbright}\Huge\$

The equation can be written as: $\displaystyle{{\left({3}{x}-{5}\right)}}^{{2}}={12}\usepackage{cmbright}\Huge\$

Use the Square Root Property: $\displaystyle{3}{x}-{5}=\pm\sqrt{{12}}=\pm\sqrt{{{4}\cdot{3}}}=\pm{2}\sqrt{{3}}\usepackage{cmbright}\Huge\$

Solve for x: $\displaystyle{3}{x}={5}\pm{2}\sqrt{{3}}\usepackage{cmbright}\Huge\$ , so $\displaystyle{x}=\frac{{5}}{{3}}\pm\frac{{2}}{{3}}\sqrt{{3}}\usepackage{cmbright}\Huge\$