t=-16t^2+84t+100

Solution for t=-16t^2+84t+100 equation:

t=-16t^2+84t+100

We move all terms to the left:

t-(-16t^2+84t+100)=0

We get rid of parentheses

16t^2-84t+t-100=0

We add all the numbers together, and all the variables

16t^2-83t-100=0

a = 16; b = -83; c = -100;
Δ = b2-4ac
Δ = -832-4·16·(-100)
Δ = 13289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-83)-\sqrt{13289}}{2*16}=\frac{83-\sqrt{13289}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-83)+\sqrt{13289}}{2*16}=\frac{83+\sqrt{13289}}{32}
$