50=-16t^2+100t-4

Solution for 50=-16t^2+100t-4 equation:

50=-16t^2+100t-4

We move all terms to the left:

50-(-16t^2+100t-4)=0

We get rid of parentheses

16t^2-100t+4+50=0

We add all the numbers together, and all the variables

16t^2-100t+54=0

a = 16; b = -100; c = +54;
Δ = b2-4ac
Δ = -1002-4·16·54
Δ = 6544
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:

$\sqrt{\Delta}=\sqrt{6544}=\sqrt{16*409}=\sqrt{16}*\sqrt{409}=4\sqrt{409}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{409}}{2*16}=\frac{100-4\sqrt{409}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{409}}{2*16}=\frac{100+4\sqrt{409}}{32}
$