t=80t-16t^2+3.5

Solution for t=80t-16t^2+3.5 equation:

t=80t-16t^2+3.5

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

16t^2-79t-3.5=0

a = 16; b = -79; c = -3.5;
Δ = b2-4ac
Δ = -792-4·16·(-3.5)
Δ = 6465
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{-(-79)-\sqrt{6465}}{2*16}=\frac{79-\sqrt{6465}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+\sqrt{6465}}{2*16}=\frac{79+\sqrt{6465}}{32}
$