Найдите корни уравнения: (x+2)^2=43-6x.

\[(x + 2)^{2} = 43 - 6x\]

\[x^{2} + 4x + 4 = 43 - 6x\]

\[x^{2} + 4x + 4 - 43 + 6x = 0\]

\[x² + 10x - 39 = 0\ \]

\[D = b^{2} - 4ac =\]

\[= 100 - 4 \cdot 1 \cdot ( - 39) =\]

\[= 100 + 156 = 256\]

\[x_{1} = \frac{- 10 + 16}{2} = \frac{6}{2} = 3\]

\[x_{2} = \frac{- 10 - 16}{2} = - \frac{26}{2} = - 13\]

\[Ответ:x_{1} = 3;\ \ x_{2} = - 13.\]