0=-16t^2+900t+6000

Solution for 0=-16t^2+900t+6000 equation:

0=-16t^2+900t+6000

We move all terms to the left:

0-(-16t^2+900t+6000)=0

We add all the numbers together, and all the variables

-(-16t^2+900t+6000)=0

We get rid of parentheses

16t^2-900t-6000=0

a = 16; b = -900; c = -6000;
Δ = b2-4ac
Δ = -9002-4·16·(-6000)
Δ = 1194000
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:

$\sqrt{\Delta}=\sqrt{1194000}=\sqrt{400*2985}=\sqrt{400}*\sqrt{2985}=20\sqrt{2985}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-20\sqrt{2985}}{2*16}=\frac{900-20\sqrt{2985}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+20\sqrt{2985}}{2*16}=\frac{900+20\sqrt{2985}}{32}
$