20=-16t^2+144t

Solution for 20=-16t^2+144t equation:

20=-16t^2+144t

We move all terms to the left:

20-(-16t^2+144t)=0

We get rid of parentheses

16t^2-144t+20=0

a = 16; b = -144; c = +20;
Δ = b2-4ac
Δ = -1442-4·16·20
Δ = 19456
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:

$\sqrt{\Delta}=\sqrt{19456}=\sqrt{1024*19}=\sqrt{1024}*\sqrt{19}=32\sqrt{19}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-32\sqrt{19}}{2*16}=\frac{144-32\sqrt{19}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+32\sqrt{19}}{2*16}=\frac{144+32\sqrt{19}}{32}
$