196=-16t^2+120t+50

Solution for 196=-16t^2+120t+50 equation:

196=-16t^2+120t+50

We move all terms to the left:

196-(-16t^2+120t+50)=0

We get rid of parentheses

16t^2-120t-50+196=0

We add all the numbers together, and all the variables

16t^2-120t+146=0

a = 16; b = -120; c = +146;
Δ = b2-4ac
Δ = -1202-4·16·146
Δ = 5056
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:

$\sqrt{\Delta}=\sqrt{5056}=\sqrt{64*79}=\sqrt{64}*\sqrt{79}=8\sqrt{79}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-8\sqrt{79}}{2*16}=\frac{120-8\sqrt{79}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+8\sqrt{79}}{2*16}=\frac{120+8\sqrt{79}}{32}
$