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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

16t^2+16t-80=0

a = 16; b = 16; c = -80;
Δ = b2-4ac
Δ = 162-4·16·(-80)
Δ = 5376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5376}=\sqrt{256*21}=\sqrt{256}*\sqrt{21}=16\sqrt{21}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16\sqrt{21}}{2*16}=\frac{-16-16\sqrt{21}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16\sqrt{21}}{2*16}=\frac{-16+16\sqrt{21}}{32}
$