50=-16t^2+122t

Solution for 50=-16t^2+122t equation:

50=-16t^2+122t

We move all terms to the left:

50-(-16t^2+122t)=0

We get rid of parentheses

16t^2-122t+50=0

a = 16; b = -122; c = +50;
Δ = b2-4ac
Δ = -1222-4·16·50
Δ = 11684
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:

$\sqrt{\Delta}=\sqrt{11684}=\sqrt{4*2921}=\sqrt{4}*\sqrt{2921}=2\sqrt{2921}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-122)-2\sqrt{2921}}{2*16}=\frac{122-2\sqrt{2921}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-122)+2\sqrt{2921}}{2*16}=\frac{122+2\sqrt{2921}}{32}
$