50=96t-16t^2

Solution for 50=96t-16t^2 equation:

50=96t-16t^2

We move all terms to the left:

50-(96t-16t^2)=0

We get rid of parentheses

16t^2-96t+50=0

a = 16; b = -96; c = +50;
Δ = b2-4ac
Δ = -962-4·16·50
Δ = 6016
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:

$\sqrt{\Delta}=\sqrt{6016}=\sqrt{64*94}=\sqrt{64}*\sqrt{94}=8\sqrt{94}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-8\sqrt{94}}{2*16}=\frac{96-8\sqrt{94}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+8\sqrt{94}}{2*16}=\frac{96+8\sqrt{94}}{32}
$