[tex]a)\\4x^{2}+8x = 0\\\\4x(x+2) = 0 \ \ /:4\\\\x(x+2) = 0\\\\x = 0 \ \vee \ x+2 = 0\\\\x = 0 \ \vee \ x = -2[/tex]
[tex]b)\\4x^{2}-9 = 0\\\\(2x+3)(2x-3) = 0\\\\2x+3 = 0 \ \vee \ 2x-3 = 0\\\\2x = -3 \ \vee \ 2x = 3\\\\x = -\frac{3}{2} \ \vee \ x = \frac{3}{2}\\\\x = -1\frac{1}{2} \ \vee \ x = 1\frac{1}{2}[/tex]
[tex]c)\\2x-5x^{2} = 0 \ \ /\cdot(-1)\\\\5x^{2}-2x = 0\\\\x(5x-2) = 0\\\\x = 0 \ \vee \ 5x-2 = 0\\\\x = 0 \ \vee \ 5x = 2 \ \ /:5\\\\x = 0 \ \vee \ x = \frac{2}{5}[/tex]
[tex]d)\\x^{2}+6 = 0\\\\x^{2}=-6, \ sprzecznosc, \ brak \ miejsc \ zerowych\\\\x^{2}\neq -6[/tex]
[tex]e)\\x^{2}+4x+3 = 0\\\\a = 1, \ b = 4, \ c = 3\\\\\Delta = b^{2}-4ac = 4^{2}-4\cdot1\cdot3 = 16 - 12 = 4\\\\\sqrt{\Delta} = \sqrt{4} = 2\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-4-2}{2\cdot1} = \frac{-6}{2} = -3\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{-4+2}{2} = \frac{-2}{2} = -1[/tex]
[tex]f)\\2x^{2}+2x-4 = 0 \ \ /:2\\\\\underline{x^{2}+x-2 = 0}\\\\a = 1, \ b = 1, \ c = -2\\\\\Delta = b^{2}-4ac=1^{2}-4\cdot1\cdot(-2) = 1+8 = 9\\\\\sqrt{\Delta} = \sqrt{9} = 3\\\\x_1 = \frac{-1-3}{2\cdot1} = \frac{-4}{2} = -2\\\\x_2 = \frac{-1+3}{2} = \frac{2}{2} = 1[/tex]
[tex]g)\\-4x^{2}-x+3 = 0 \ \ /\cdot(-1)\\\\\underline{4x^{2}+x-3 = 0}\\\\a = 4, \ b = 1, \ c = -3\\\\\Delta = b^{2}-4ac = 1^{2}-4\cdot4\cdot(-3) =1+48 = 49\\\\\sqrt{\Delta} = \sqrt{49} = 7\\\\x_1 = \frac{-1-7}{2\cdot4}=\frac{-8}{8} = -1\\\\x_2 = \frac{-1+7}{8} = \frac{6}{8} = \frac{3}{4}[/tex]
