Найдите количество целых корней уравнения |x^2-7x-8|:(x^2-7x-8)=|x^2+2x-8|:(-x^2-2x+8)

[latex]x^2-7x-8 = 0, \ x_1=-1, x_2=8; \ x^2+2x-8=0, \ x_1=-4, x_2=2; \ \ x extless -4, \ x^2-7x-8 extgreater 0, x^2+2x-8 extgreater 0, \ (x^2-7x-8):(x^2-7x-8)=(x^2+2x-8):(-x^2-2x+8), \ 1=-1, \ 0cdot x = -2, \ xinvarnothing; \ \ -4 extless x extless -1, \ x^2-7x-8 extgreater 0, x^2+2x-8 extless 0, \ (x^2-7x-8):(x^2-7x-8)=-(x^2+2x-8):(-x^2-2x+8), \ 1=1, \ 0cdot x = 0, \ xin R, \ xin(-4;-1); \ \ -1 extless x extless 2, \ x^2-7x-8 extless 0, x^2+2x-8 extless 0, \ -(x^2-7x-8):(x^2-7x-8)=-(x^2+2x-8):(-x^2-2x+8), \ -1=1, \ 0cdot x = 2, \ xinvarnothing; \ \[/latex][latex]2 extless x extless 8, \ x^2-7x-8 extless 0, x^2+2x-8 extgreater 0, \ -(x^2-7x-8):(x^2-7x-8)=(x^2+2x-8):(-x^2-2x+8), \ -1=-1, \ 0cdot x = 0, \ xin R; \ xin(2;8); \ \ x extgreater 8, \ x^2-7x-8 extgreater 0, x^2+2x-8 extgreater 0, \ (x^2-7x-8):(x^2-7x-8)=(x^2+2x-8):(-x^2-2x+8), \ 1=-1, \ 0cdot x = -2, \ xinvarnothing; \ \ xin(-4;-1)cup(2;8); \ X_Z={-3, -2, 3, 4, 5, 6, 7}, \ 7.[/latex]