(5x^2-6x-8)-(x^2+2x-15)
=5x^2-6x-8-x^2-2x+15
=4x^2-8x+7
=4(x^2-2x+1)+3
=4(x-2)^2+3>0
5x^2-6x-8>x^2+2x-15