[tex]x^2 + 6 x -14= 0 \\a=1, \ \ b=6, \ \ c=-14 \\ \\\Delta =b^2-4ac = 6^2 -4\cdot1\cdot (-14) = 36+56=92 \\ \\x_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{-6-\sqrt{92}}{2 }=\frac{ -6- \sqrt{23\cdot 4}}{2}= \frac{ -6- 2\sqrt{23 }}{2}= \\\\=\frac{ 2(-3- \sqrt{23 })}{2}= -3- \sqrt{23 }[/tex]
[tex]x_{2}=\frac{-b+\sqrt{\Delta} }{2a}=\frac{-6+\sqrt{92}}{2 }=\frac{ -6+ \sqrt{23\cdot 4}}{2}= \frac{ -6+ 2\sqrt{23 }}{2}= \\\\=\frac{ 2(-3+ \sqrt{23 })}{2}= -3+\sqrt{23 } \\\\x_{1}+x_{2}=-3-\sqrt{23 } -3+\sqrt{23 } = -6[/tex]
