Answer
$(-∞, -3/2)$ U $(5, ∞)$
Work Step by Step
$2x^2-7x >15$
$2x^2-7x-15 >15-15$
$2x^2-7x-15 >0$
$(2x+3)(x-5) >0$
$2x+3=0$
$2x+3-3=0-3$
$2x=-3$
$2x/2=-3/2$
$x=-3/2$
$x-5=0$
$x-5+5=0+5$
$x=5$
Three regions to test: $(-∞, -3/2)$, $(-3/2, 5)$, $(5, ∞)$
Let $x=-10$, $x=0$, $x=10$
$x=-10$
$2(-10)^2-7(-10) >15$
$2*100+70 >15$
$270 > 15$ (true)
$x=0$
$2x^2-7x >15$
$2*0^2-7*0 >15$
$2*0 -0 >15$
$0-0 > 15$
$0 > 15$ (false)
$x=10$
$2x^2-7x >15$
$2(10)^2-7(10) >15$
$2*100-70 >15$
$200-70 > 15$ (true)
$130 > 15$ (true)
