Сумма целых решений неравенства |2x²+6x+1|≤x²-3x-19

" alt="|2x^{2} +6x+1| \leq x^{2} -3x-19 \\ \\ \left \{ {{2 x^{2} +6x+1 \leq x^{2} -3x-19} \atop {2 x^{2} +6x+1 \geq 0}} \right. \\ \left \{ {{x^{2} +9x+20 \leq 0} \atop {2 x^{2} +6x+1 \geq 0}} \right. \\ x^{2} +9x+20 =0, x_{1}=-4,x_{2}=-5 \\ 2 x^{2} +6x+1=0, \\ D=28, \sqrt{D} = \sqrt{28}=2 \sqrt{7} \\ x_{1}= \frac{-3+ \sqrt{7} }{2} ,x_{2}= \frac{-3- \sqrt{7} }{2} \\ " align="absmiddle" class="latex-formula">
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_____-5____________-4__________(-3-√7)/2________(-3+√7)/2___0______
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решение первой системы -5 ≤ Х ≤ -4

$\\ \left \{ {{-2 x^{2} -6x-1 \leq x^{2} -3x-19} \atop {2 x^{2} +6x+1< 0}} \right. \\ \left \{ {{-3x^{2} -3x+18 \leq 0} \atop {2 x^{2} +6x+1 < 0}} \right. \\ \left \{ {{x^{2} +x-6 \geq 0} \atop {2 x^{2} +6x+1 < 0}} \right. \\ x^{2} + x - 6 =0, x_{1}=-3,x_{2}=2 \\$
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_____-3_____(-3-√7)/2________(-3+√7)/2___0________ 2________
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решений нет

Таким образом решение системы -5 ≤ Х ≤ -4.
Тогда сумма целых решений: (-4) + (-5) = -9
Ответ: -9.