[tex]x^2+6x-7=0 \\ a=1 \\ b= 6 \\ c=-7 \\ \\ \boxed{\boxed{\Delta=b^2-4ac}} \\ \\ \Delta=6^2-4*1*(-7) \\ \Delta=36-(-28) \\ \Delta=64 \\ \Delta\ \textgreater \ 0 \Rightarrow \text{we have 2 solutions :} X_1 \ and X_2 \\ \\ \boxed{X_1= \frac{-b- \sqrt{\Delta} }{2a} } \Rightarrow X_1= \frac{-6-8}{2}=-7 \\ \\ \boxed{X_2= \frac{-b+ \sqrt{\Delta} }{2a} } \Rightarrow X_2= \frac{-6+8}{2} =1 [/tex]
