200=16t2+64t+192

Solution for 200=16t2+64t+192 equation:

200=16t^2+64t+192

We move all terms to the left:

200-(16t^2+64t+192)=0

We get rid of parentheses

-16t^2-64t-192+200=0

We add all the numbers together, and all the variables

-16t^2-64t+8=0

a = -16; b = -64; c = +8;
Δ = b2-4ac
Δ = -642-4·(-16)·8
Δ = 4608
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:

$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-48\sqrt{2}}{2*-16}=\frac{64-48\sqrt{2}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+48\sqrt{2}}{2*-16}=\frac{64+48\sqrt{2}}{-32}
$