Question

How do you solve `3x^2+16x<-5`?

Answer 1

The answer is `x in] -5,-1/3 [`

Explanation:

Let's rewrite the inequality `f(x)=3x^2+16x+5=(3x+1)(x+5)<0`
Let's do a sign chart
`color(white)(aaaa)` `x` `color(white)(aaaa)` `-oo` `color(white)(aaaa)` `-5` `color(white)(aaaa)` `-1/3` `color(white)(aaaa)` `+oo`
`color(white)(aaaa)` `x+5` `color(white)(aaaaa)` `-` `color(white)(aaaaa)` `+` `color(white)(aaaaa)` `+`
`color(white)(aaaa)` `3x+1` `color(white)(aaaa)` `-` `color(white)(aaaaa)` `-` `color(white)(aaaaa)` `+`
`color(white)(aaaa)` `f(x)` `color(white)(aaaaaa)` `+` `color(white)(aaaaa)` `-` `color(white)(aaaaa)` `+`
So the answer is `x in] -5,(-1/3) [`
graph{3x^2+16x+5 [-22.8, 22.83, -11.4, 11.4]}