0=-140+96t-16t^2

Solution for 0=-140+96t-16t^2 equation:

0=-140+96t-16t^2

We move all terms to the left:

0-(-140+96t-16t^2)=0

We add all the numbers together, and all the variables

-(-140+96t-16t^2)=0

We get rid of parentheses

16t^2-96t+140=0

a = 16; b = -96; c = +140;
Δ = b2-4ac
Δ = -962-4·16·140
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-16}{2*16}=\frac{80}{32}
=2+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+16}{2*16}=\frac{112}{32}
=3+1/2
$