100t=-16t^2+128t+1

Solution for 100t=-16t^2+128t+1 equation:

100t=-16t^2+128t+1

We move all terms to the left:

100t-(-16t^2+128t+1)=0

We get rid of parentheses

16t^2-128t+100t-1=0

We add all the numbers together, and all the variables

16t^2-28t-1=0

a = 16; b = -28; c = -1;
Δ = b2-4ac
Δ = -282-4·16·(-1)
Δ = 848
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:

$\sqrt{\Delta}=\sqrt{848}=\sqrt{16*53}=\sqrt{16}*\sqrt{53}=4\sqrt{53}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{53}}{2*16}=\frac{28-4\sqrt{53}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{53}}{2*16}=\frac{28+4\sqrt{53}}{32}
$