120=-16t^2+64t+60

Solution for 120=-16t^2+64t+60 equation:

120=-16t^2+64t+60

We move all terms to the left:

120-(-16t^2+64t+60)=0

We get rid of parentheses

16t^2-64t-60+120=0

We add all the numbers together, and all the variables

16t^2-64t+60=0

a = 16; b = -64; c = +60;
Δ = b2-4ac
Δ = -642-4·16·60
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-16}{2*16}=\frac{48}{32}
=1+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+16}{2*16}=\frac{80}{32}
=2+1/2
$