50=80t-16t^2

Solution for 50=80t-16t^2 equation:

50=80t-16t^2

We move all terms to the left:

50-(80t-16t^2)=0

We get rid of parentheses

16t^2-80t+50=0

a = 16; b = -80; c = +50;
Δ = b2-4ac
Δ = -802-4·16·50
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-40\sqrt{2}}{2*16}=\frac{80-40\sqrt{2}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+40\sqrt{2}}{2*16}=\frac{80+40\sqrt{2}}{32}
$