[tex]3x^2+7=0
\\x^2=- \frac{7}{3}
\\x=\pm \sqrt{-\frac{7}{3} }
\\x=\pm i \sqrt{\frac{7}{3} }
\\
\\(x- \frac{1}{3} )^2=x^2- \frac{2}{3}x+ \frac{1}{9} =- \frac{7}{3} -\frac{2}{3}(\pm i \sqrt{\frac{7}{3} } )+ \frac{1}{9} =
\\=- \frac{21}{9} -\frac{2}{3}(\pm i \sqrt{\frac{7}{3} } )+ \frac{1}{9}
\\=- \frac{20}{9} \mp i\frac{2}{3} \sqrt{\frac{7}{3} }
[/tex]
