Inequality Word Problem

Question

If a Baseball is thrown straight upward from level ground with an intial velocity of $72$ ft/sec, its altitude $s$ (in feet) after $t$ seconds is given by $s = -16t^2 + 72t$. For what values of $t$ will the ball be at least $32$ feet above the ground?

I know the answer only which $1/2<t\leq4$ but i don't know the steps

Answer 1

hint: Solve: $-16t^2 + 72t \ge 32$.

Answer 2

We want $s\geq 32$

or

$-16t^2+72t-32\geq 0$

$\iff -2t^2+9t-4\geq 0$

the discriminant is

$\Delta=81-32=49$

the roots are $4$ and $\frac{1}{2}$.

the answer is $\frac{1}{2}$.