Решить уравнение:(2х - 1) (2х + 1) + х (х - 1) = 2х (х + 1)

[latex](2x - 1) (2x + 1) + x (x - 1) = 2x (x + 1)[/latex] [latex]\left( 2 x-1 \right) \left( 2 x+1 \right) +x \left( x-1 \right) -2 x \left( x+1 \right) = 0[/latex] [latex]4 x^2+2 x-2 x-1+x^2+x \left( -1 \right) -2 x^2-2 x= 0[/latex] [latex]3 x^2-3 x-1 = 0[/latex]  [latex]x_{1,2}= \frac{-b\pm\sqrt{D}}{2a} = \frac{3\pm\sqrt{21}}{6} = \frac{3\pm\sqrt{21}}{6}[/latex] [latex]x_1 = \frac{3+\sqrt{21}}{6},\; x_2 = \frac{3-\sqrt{21}}{6}[/latex]

4X^2 - 1 + X^2 - X = 2X^2 + 2X  5X^2 - 2X^2 - X - 2X - 1 = 0 3X^2 - 3X - 1 = 0 D = 9 -4*3*(-1) = 9 + 12 = 21  X1 = ( 3 + V 21 ) \ 6  X2 = ( 3 - V 21 ) \ 6