0(t)=80+64t-16t2

Solution for 0(t)=80+64t-16t2 equation:

0(t)=80+64t-16t^2

We move all terms to the left:

0(t)-(80+64t-16t^2)=0

We add all the numbers together, and all the variables

-(80+64t-16t^2)+t=0

We get rid of parentheses

16t^2-64t+t-80=0

We add all the numbers together, and all the variables

16t^2-63t-80=0

a = 16; b = -63; c = -80;
Δ = b2-4ac
Δ = -632-4·16·(-80)
Δ = 9089
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{-(-63)-\sqrt{9089}}{2*16}=\frac{63-\sqrt{9089}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{9089}}{2*16}=\frac{63+\sqrt{9089}}{32}
$