[tex]m^2+2m-48=-6 \\ \\ m^2+2m-48+6=0\\ \\m^2+2m-42=0\\ \\a=1, \ b= 2, \ c= -42 \\ \\\Delta = b^{2}-4ac = 2^{2}-4*1*(-42)= 4+168 =172 \\\\\sqrt{\Delta }=\sqrt{172} =\sqrt{4*43}=2\sqrt{43}\\ \\x_{1}=\frac{-b-\sqrt{\Delta }}{2a} =\frac{-2-2\sqrt{43}}{2}=\frac{2(-1-\sqrt{43})}{2}= -1-\sqrt{43} \\ \\x_{2}=\frac{-b+\sqrt{\Delta }}{2a} = \frac{-2+2\sqrt{43}}{2}=\frac{ 2(-1+\sqrt{43})}{2}= -1+\sqrt{43}[/tex]
