x(2x-1)=(1-2x)(1+2x)
x(2x-1)=-(2x-1)(1+2x)
x(2x-1)+(2x-1)(1+2x)=0
(2x-1)(x+1+2x)=0
2(x-½)(3x+1)=0
(x-½)(x+⅓)=0
x=½ lub x=-⅓
[tex]x(2x-1) = (1-2x)(1+2x)\\\\2x^{2}-x = 1 - 4x^{2}\\\\2x^{2}+4x^{2}-x-1 = 0\\\\6x^{2}-x-1 = 0\\\\a = 6, \ b = -1, \ c = -1\\\\\Delta = b^{2}-4ac = (-1)^{2}-4\cdot6\cdot(-1) = 1+24 = 25\\\\\sqrt{\Delta} = \sqrt{25} = 5\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-(-1)-5}{2\cdot6} = \frac{-4}{12} = -\frac{1}{3}\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{-(-1)+5}{12} = \frac{6}{12} = \frac{1}{2}\\\\x \in\{-\frac{1}{3}; \frac{1}{2}\}[/tex]
