0=120t-5t^2

Solution for 0=120t-5t^2 equation:

0=120t-5t^2

We move all terms to the left:

0-(120t-5t^2)=0

We add all the numbers together, and all the variables

-(120t-5t^2)=0

We get rid of parentheses

5t^2-120t=0

a = 5; b = -120; c = 0;
Δ = b2-4ac
Δ = -1202-4·5·0
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-120}{2*5}=\frac{0}{10}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+120}{2*5}=\frac{240}{10}
=24
$