[tex]9x ^{2}-6x-11=0 \\ \\ a=9 , \ b=-6, \ c = -11 \\ \\ \Delta = b^{2}-4ac = (-6)^{2}-4*9* (-11)= 36+396 = 432\\ \\\sqrt{\Delta }=\sqrt{432}= \sqrt{144*3}=12\sqrt{3}\\ \\x_{1}=\frac{-b-\sqrt{\Delta }}{2a} =\frac{6-12\sqrt{3}}{2*9}=\frac{ 6(2-2\sqrt{3})}{18}= \frac{ 2-2\sqrt{3} }{3} \\ \\x_{2}=\frac{-b+\sqrt{\Delta }}{2a} =\frac{6+12\sqrt{3}}{2*9}=\frac{ 6(2+2\sqrt{3})}{18}= \frac{ 2+2\sqrt{3} }{3} [/tex]
