80t-16t^2=20

Solution for 80t-16t^2=20 equation:

80t-16t^2=20

We move all terms to the left:

80t-16t^2-(20)=0

a = -16; b = 80; c = -20;
Δ = b2-4ac
Δ = 802-4·(-16)·(-20)
Δ = 5120
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:

$\sqrt{\Delta}=\sqrt{5120}=\sqrt{1024*5}=\sqrt{1024}*\sqrt{5}=32\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-32\sqrt{5}}{2*-16}=\frac{-80-32\sqrt{5}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+32\sqrt{5}}{2*-16}=\frac{-80+32\sqrt{5}}{-32}
$