30000=1500t-16t^2

Solution for 30000=1500t-16t^2 equation:

30000=1500t-16t^2

We move all terms to the left:

30000-(1500t-16t^2)=0

We get rid of parentheses

16t^2-1500t+30000=0

a = 16; b = -1500; c = +30000;
Δ = b2-4ac
Δ = -15002-4·16·30000
Δ = 330000
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:

$\sqrt{\Delta}=\sqrt{330000}=\sqrt{10000*33}=\sqrt{10000}*\sqrt{33}=100\sqrt{33}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1500)-100\sqrt{33}}{2*16}=\frac{1500-100\sqrt{33}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1500)+100\sqrt{33}}{2*16}=\frac{1500+100\sqrt{33}}{32}
$