160t=-16t^2+16t+480

Solution for 160t=-16t^2+16t+480 equation:

160t=-16t^2+16t+480

We move all terms to the left:

160t-(-16t^2+16t+480)=0

We get rid of parentheses

16t^2-16t+160t-480=0

We add all the numbers together, and all the variables

16t^2+144t-480=0

a = 16; b = 144; c = -480;
Δ = b2-4ac
Δ = 1442-4·16·(-480)
Δ = 51456
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:

$\sqrt{\Delta}=\sqrt{51456}=\sqrt{256*201}=\sqrt{256}*\sqrt{201}=16\sqrt{201}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-16\sqrt{201}}{2*16}=\frac{-144-16\sqrt{201}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+16\sqrt{201}}{2*16}=\frac{-144+16\sqrt{201}}{32}
$