[tex] x^2 - 6x - 27 = 0 \\ \\a=1, \ b=-6 , \ c= -27 \\ \\ \Delta =b^2-4ac = (-6)^2 -4\cdot1\cdot (-27) = 36+108 =144 \\ \\x_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{6-\sqrt{144}}{2 }=\frac{ 6-12}{2}=\frac{-6}{2}=-3 \\ \\x_{2}=\frac{-b+\sqrt{\Delta }}{2a}= \frac{6+\sqrt{144}}{2 }=\frac{ 6+12}{2}= \frac{18}{2}=9 \\ \\ \\ Answer : \ x= -3 \ \ or \ \ x= 9 [/tex]
