1.
[tex](2x-3)(x+4)-(2x-3)(x-1)-(2x-3)(x+5) = 0\\\\(2x-3)[(x+4)-(x-1)-(x+5)] = 0\\\\(2x-3)(x+4-x+1-x-5) = 0\\\\(2x-3)(-x) = 0 \ \ /\cdot(-1)\\\\x(2x-3) = 0\\\\x = 0 \ \vee \ 2x-3 = 0\\\\x = 0 \ \vee \ 2x = 3\\\\x = 0 \ \vee \ x = 1,5\\\\x \in\{0;1,5\}[/tex]
2.
[tex]-x(4x-x) > 4 - x^{2}\\\\-4x^{2}+x^{2}>4-x^{2}\\\\-3x^{2}+x^{2} > 4\\\\-2x^{2} > 4 \ \ /:(-2)\\\\x^{2} < -4, \ sprzecznosc, \ brak \ rozwiazan[/tex]
3.
[tex]x^{4}+2x^{2}-15 = 0\\\\x^{4}-3x^{2}+5x^{2}-15 = 0\\\\x^{2}(x^{2}-3) + 5(x^{2}-3) = 0\\\\(x^{2}-3)(x^{2}+5) = 0\\\\x^{2}-3 = 0, \ \ \ x^{2}+5 > 0\\\\(x+\sqrt{3})(x-\sqrt{3}) = 0\\\\x = -\sqrt{3} \ \vee \ x = \sqrt{3}\\\\x \in \{-\sqrt{3};\sqrt{3}\}[/tex]
