# Prove or disprove inequality using other inequality

if $3x^2+2ax+b+5\sin 2x >0$, then prove/disprove that $a^2-3b+15<0$.($x\in \mathbb R$)

If disproven find correct inequality relating $a,b$

I don't know where to start. Any hint will be appreciated

In the best case $$3x^2+2ax+b+5>0$$ Thus, the quadratic form does not change in sign and has no root $$\Delta<0$$
$$(2a)^2-4(3)(b+5)<0$$
$$a^2-(3)(b+5)<0$$