1=-16t^2+100t+50

Solution for 1=-16t^2+100t+50 equation:

1=-16t^2+100t+50

We move all terms to the left:

1-(-16t^2+100t+50)=0

We get rid of parentheses

16t^2-100t-50+1=0

We add all the numbers together, and all the variables

16t^2-100t-49=0

a = 16; b = -100; c = -49;
Δ = b2-4ac
Δ = -1002-4·16·(-49)
Δ = 13136
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:

$\sqrt{\Delta}=\sqrt{13136}=\sqrt{16*821}=\sqrt{16}*\sqrt{821}=4\sqrt{821}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{821}}{2*16}=\frac{100-4\sqrt{821}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{821}}{2*16}=\frac{100+4\sqrt{821}}{32}
$