0=-16t^2-120t-50

Solution for 0=-16t^2-120t-50 equation:

0=-16t^2-120t-50

We move all terms to the left:

0-(-16t^2-120t-50)=0

We add all the numbers together, and all the variables

-(-16t^2-120t-50)=0

We get rid of parentheses

16t^2+120t+50=0

a = 16; b = 120; c = +50;
Δ = b2-4ac
Δ = 1202-4·16·50
Δ = 11200
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:

$\sqrt{\Delta}=\sqrt{11200}=\sqrt{1600*7}=\sqrt{1600}*\sqrt{7}=40\sqrt{7}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-40\sqrt{7}}{2*16}=\frac{-120-40\sqrt{7}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+40\sqrt{7}}{2*16}=\frac{-120+40\sqrt{7}}{32}
$