t=80-16t2+3.5

Solution for t=80-16t2+3.5 equation:

t=80-16t^2+3.5

We move all terms to the left:

t-(80-16t^2+3.5)=0

We get rid of parentheses

16t^2+t-80-3.5=0

We add all the numbers together, and all the variables

16t^2+t-83.5=0

a = 16; b = 1; c = -83.5;
Δ = b2-4ac
Δ = 12-4·16·(-83.5)
Δ = 5345
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{-(1)-\sqrt{5345}}{2*16}=\frac{-1-\sqrt{5345}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{5345}}{2*16}=\frac{-1+\sqrt{5345}}{32}
$