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

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

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

We move all terms to the left:

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

We get rid of parentheses

16t^2-60t+t=0

We add all the numbers together, and all the variables

16t^2-59t=0

a = 16; b = -59; c = 0;
Δ = b2-4ac
Δ = -592-4·16·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-59}{2*16}=\frac{0}{32}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+59}{2*16}=\frac{118}{32}
=3+11/16
$