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

Solution for A(t)=-16t^2+64t+80 equation:

(A)=-16A^2+64A+80

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

16A^2-63A-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:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-\sqrt{9089}}{2*16}=\frac{63-\sqrt{9089}}{32}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{9089}}{2*16}=\frac{63+\sqrt{9089}}{32}
$