6=120t-16t^2

Solution for 6=120t-16t^2 equation:

6=120t-16t^2

We move all terms to the left:

6-(120t-16t^2)=0

We get rid of parentheses

16t^2-120t+6=0

a = 16; b = -120; c = +6;
Δ = b2-4ac
Δ = -1202-4·16·6
Δ = 14016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14016}=\sqrt{64*219}=\sqrt{64}*\sqrt{219}=8\sqrt{219}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-8\sqrt{219}}{2*16}=\frac{120-8\sqrt{219}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+8\sqrt{219}}{2*16}=\frac{120+8\sqrt{219}}{32}
$