0=-16t^2+24t+160

Solution for 0=-16t^2+24t+160 equation:

0=-16t^2+24t+160

We move all terms to the left:

0-(-16t^2+24t+160)=0

We add all the numbers together, and all the variables

-(-16t^2+24t+160)=0

We get rid of parentheses

16t^2-24t-160=0

a = 16; b = -24; c = -160;
Δ = b2-4ac
Δ = -242-4·16·(-160)
Δ = 10816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10816}=104$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-104}{2*16}=\frac{-80}{32}
=-2+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+104}{2*16}=\frac{128}{32}
=4
$