Given a quadratic equation [tex]ax^2+bx+c=0[/tex], the two solution (if they exist) are given by the formula
[tex]x_{1,2}=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In your case, the coefficients are
[tex]a=3,\quad b=5,\quad c=2[/tex]
So the quadratic formula becomes
[tex]x_{1,2}=\dfrac{-5\pm\sqrt{25-24}}{6} = \dfrac{-5\pm 1}{6}[/tex]
So, the two solutions are
[tex]x_1 = \dfrac{-5+1}{6}=-\dfrac{4}{6}=-\dfrac{2}{3}[/tex]
[tex]x_2 = \dfrac{-5-1}{6}=-\dfrac{6}{6}=-1[/tex]
