Найдите корни уравнения: (x^2+2x)/2=(x^2+24)/7.

Ответ:

\[\frac{x^{2} + 2x}{2} = \frac{x^{2} + 24}{7}\ \ \ \ \ | \cdot 14\]

\[7 \cdot \left( x^{2} + 2x \right) = 2 \cdot \left( x^{2} + 24 \right)\]

\[7x^{2} + 14x = 2x^{2} + 48\]

\[5x^{2} + 14x - 48 = 0\]

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

\[= 196 - 4 \cdot 5 \cdot ( - 48) =\]

\[= 196 + 960 = 1156\]

\[x_{1} = \frac{- 14 + 34}{10} = \frac{20}{10} = 2\]

\[x_{2} = \frac{- 14 - 34}{10} = - \frac{48}{10} = - 4,8\]

\[Ответ:x = 2\ \ и\ \ \ x = - 4,8.\]