Answer
$(-∞, -3/2)$ U $(5, ∞)$
Work Step by Step
$2x^2-7x >15$
$2x^2-7x-15>15-15$
$2x^2-7x-15>0$
$(2x+3)(x-5) >0$
$2x+3=0$
$2x+3-3=0-3$
$2x=-3$
$2x/2=-3/2$
$x=-3/2$
$x-5=0$
$x-5+5=5$
$x=5$
Three regions to test: $(-∞, -3/2)$, $(3/2, 5)$, $(5, ∞)$
Let $x=-2$, $x=2$, $x=6$
$x=-2$
$2x^2-7x >15$
$2(-2)^2-7*(-2) >15$
$2*4+14>15$
$8+14 > 15$
$22 > 15 (true)
$x=0$
$2x^2-7x >15$
$2*0^2-7*0 >15$
$2*0-0 >15$
$0-0 > 15$
$0 > 15$ (false)
$x=6$
$2x^2-7x >15$
$2*6^2-7*6 >15$
$2*36-42 > 15$
$72-42 > 15$
$30 > 15$ (true)
$(-∞, -3/2)$ U $(5, ∞)$
