0=-16t^2+476t+120t

Solution for 0=-16t^2+476t+120t equation:

0=-16t^2+476t+120t

We move all terms to the left:

0-(-16t^2+476t+120t)=0

We add all the numbers together, and all the variables

-(-16t^2+476t+120t)=0

We get rid of parentheses

16t^2-476t-120t=0

We add all the numbers together, and all the variables

16t^2-596t=0

a = 16; b = -596; c = 0;
Δ = b2-4ac
Δ = -5962-4·16·0
Δ = 355216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{355216}=596$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-596)-596}{2*16}=\frac{0}{32}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-596)+596}{2*16}=\frac{1192}{32}
=37+1/4
$