Question

Решите уравнение
3(x+1)(x+5)=2x²+10x
Нужен ответ без решения

Answer 1

Ответ:

-5; -3

Пошаговое объяснение:

$3(x + 1)(x + 5) = 2x {}^{2} + 10x \\ (3x + 3)(x + 5) = 2x {}^{2} + 10x \\ 3x {}^{2} + 15x + 3x + 15 = 2x {}^{2} + 10x \\ 3x {}^{2} + 18x + 15 = 2x {}^{2} + 10x \\ 3x {}^{2} + 18x + 15 - 2x {}^{2} - 10x = 0 \\ x {}^{2} + 8x + 15 = 0 \\ D = b {}^{2} - 4ac = 64 - 60 = 4 = 2 {}^{2} \\ x_{1 ;2} = \displaystyle \frac{ - b \pm \sqrt{D} }{2a} \Rightarrow \\ x_{1} = \frac{ - 8 - 2}{2} = \frac{ - 10}{2} = - 5 \\ x_{2} = \frac{ - 8 + 2}{2} = \frac{ - 6}{2} = - 3$