120=-16t2+64t+80

Solution for 120=-16t2+64t+80 equation:

120=-16t^2+64t+80

We move all terms to the left:

120-(-16t^2+64t+80)=0

We get rid of parentheses

16t^2-64t-80+120=0

We add all the numbers together, and all the variables

16t^2-64t+40=0

a = 16; b = -64; c = +40;
Δ = b2-4ac
Δ = -642-4·16·40
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-16\sqrt{6}}{2*16}=\frac{64-16\sqrt{6}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+16\sqrt{6}}{2*16}=\frac{64+16\sqrt{6}}{32}
$