30=-16t^2+16t+480

Solution for 30=-16t^2+16t+480 equation:

30=-16t^2+16t+480

We move all terms to the left:

30-(-16t^2+16t+480)=0

We get rid of parentheses

16t^2-16t-480+30=0

We add all the numbers together, and all the variables

16t^2-16t-450=0

a = 16; b = -16; c = -450;
Δ = b2-4ac
Δ = -162-4·16·(-450)
Δ = 29056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{29056}=\sqrt{64*454}=\sqrt{64}*\sqrt{454}=8\sqrt{454}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{454}}{2*16}=\frac{16-8\sqrt{454}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{454}}{2*16}=\frac{16+8\sqrt{454}}{32}
$