480=100t-5t^2

Solution for 480=100t-5t^2 equation:

480=100t-5t^2

We move all terms to the left:

480-(100t-5t^2)=0

We get rid of parentheses

5t^2-100t+480=0

a = 5; b = -100; c = +480;
Δ = b2-4ac
Δ = -1002-4·5·480
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20}{2*5}=\frac{80}{10}
=8
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20}{2*5}=\frac{120}{10}
=12
$