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

$(2x - 1) (2x + 1) + x (x - 1) = 2x (x + 1)$

$\left( 2 x-1 \right) \left( 2 x+1 \right) +x \left( x-1 \right) -2 x \left( x+1 \right) = 0$

$4 x^2+2 x-2 x-1+x^2+x \left( -1 \right) -2 x^2-2 x= 0$

$3 x^2-3 x-1 = 0$

$x_{1,2}= \frac{-b\pm\sqrt{D}}{2a} = \frac{3\pm\sqrt{21}}{6} = \frac{3\pm\sqrt{21}}{6}$

$x_1 = \frac{3+\sqrt{21}}{6},\; x_2 = \frac{3-\sqrt{21}}{6}$