0=-16t^2+300t+200

Solution for 0=-16t^2+300t+200 equation:

0=-16t^2+300t+200

We move all terms to the left:

0-(-16t^2+300t+200)=0

We add all the numbers together, and all the variables

-(-16t^2+300t+200)=0

We get rid of parentheses

16t^2-300t-200=0

a = 16; b = -300; c = -200;
Δ = b2-4ac
Δ = -3002-4·16·(-200)
Δ = 102800
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:

$\sqrt{\Delta}=\sqrt{102800}=\sqrt{400*257}=\sqrt{400}*\sqrt{257}=20\sqrt{257}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-20\sqrt{257}}{2*16}=\frac{300-20\sqrt{257}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+20\sqrt{257}}{2*16}=\frac{300+20\sqrt{257}}{32}
$