Answer: First Option[tex]x_1=-\frac{2}{3}[/tex] and [tex]x_2=-3[/tex] Step-by-step explanation:We have the following quadratic equation:[tex]3x^2 +11x+6=0[/tex]To solve this equation use the quadratic formulaFor an equation of the form:[tex]ax ^ 2 + bx + c = 0[/tex]The quadratic formula is:[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]Note that in this case: [tex]a=3,\ b=11,\ c=6[/tex]Then:[tex]x=\frac{-11\±\sqrt{11^2-4(3)(6)}}{2(3)}[/tex][tex]x=\frac{-11\±\sqrt{121-72}}{6}[/tex][tex]x=\frac{-11\±\sqrt{49}}{6}[/tex][tex]x=\frac{-11\±7}{6}[/tex][tex]x_1=\frac{-11+7}{6}[/tex][tex]x_1=-\frac{2}{3}[/tex][tex]x_2=\frac{-11-7}{6}[/tex][tex]x_2=\frac{-18}{6}[/tex][tex]x_2=-3[/tex]The solutions are: [tex]x_1=-\frac{2}{3}[/tex] and [tex]x_2=-3[/tex]