120t-16t^2=216

Solution for 120t-16t^2=216 equation:

120t-16t^2=216

We move all terms to the left:

120t-16t^2-(216)=0

a = -16; b = 120; c = -216;
Δ = b2-4ac
Δ = 1202-4·(-16)·(-216)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-24}{2*-16}=\frac{-144}{-32}
=4+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+24}{2*-16}=\frac{-96}{-32}
=+3
$