0=-16t^2+160t-384

Solution for 0=-16t^2+160t-384 equation:

0=-16t^2+160t-384

We move all terms to the left:

0-(-16t^2+160t-384)=0

We add all the numbers together, and all the variables

-(-16t^2+160t-384)=0

We get rid of parentheses

16t^2-160t+384=0

a = 16; b = -160; c = +384;
Δ = b2-4ac
Δ = -1602-4·16·384
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-32}{2*16}=\frac{128}{32}
=4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+32}{2*16}=\frac{192}{32}
=6
$