[tex]a)\\x^{2}-4x - 5 = 0\\\\a = 1, \ b = -4, \ c = -5\\\\\Delta = b^{2}-4ac = (-4)^{2}-4\cdot1\cdot(-5) =16 + 20 = 36\\\\\sqrt{\Delta } = \sqrt{36} = 6\\\\x_1 = \frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)-6}{2\cdot1} = \frac{-2}{2} = -1\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6}{2} = \frac{10}{2} = 5\\\\x \in \{-1; 5\}[/tex]
[tex]b)\\-x^{2}+3x+4 = 0 \ \ /\cdot(-1)\\\\x^{2}-3x-4 = 0\\\\a = 1, \ b = -3, \ c = -4\\\\\Delta = b^{2}-4ac = (-3)^{2} -4\cdot1\cdot(-4) = 9+16 = 25\\\\\sqrt{\Delta} = \sqrt{25} = 5\\\\x_1 = \frac{-(-3)-5}{2\cdot1} = \frac{-2}{2} =-1\\\\x_2 = \frac{-(-3)+5}{2} = \frac{8}{2} = 4\\\\x \in \{-1;4\}[/tex]
