[tex]x^{2}+5x+6 = 0\\\\a = 1, \ b = 5, \ c = 6\\\\\Delta = b^{2}-4ac = 5^{2}-4\cdot1\cdot6 = 25-24 = 1\\\\\sqrt{\Delta} = \sqrt{1} = 1\\\\x_1 =\frac{-b-\sqrt{\Delta}}{2a} = \frac{-5-1}{2\cdot1} = \frac{-6}{2} = -3\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{-5+1}{2} = \frac{-4}{2} = -2[/tex]
