Решите уравнение: (2x-3)(x+1)=x^2+17.

\[(2x - 3)(x + 1) = x^{2} + 17\]

\[2x^{2} - 3x + 2x - 3 - x^{2} - 17 =\]

\[= 0\]

\[x^{2} - x - 20 = 0\]

\[x_{1} + x_{2} = 1;\ \ \ x_{1} \cdot x_{2} = - 20\]

\[x_{1} = 5;\ \ x_{2} = - 4.\]