200=16t^2+152t+40

Solution for 200=16t^2+152t+40 equation:

200=16t^2+152t+40

We move all terms to the left:

200-(16t^2+152t+40)=0

We get rid of parentheses

-16t^2-152t-40+200=0

We add all the numbers together, and all the variables

-16t^2-152t+160=0

a = -16; b = -152; c = +160;
Δ = b2-4ac
Δ = -1522-4·(-16)·160
Δ = 33344
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:

$\sqrt{\Delta}=\sqrt{33344}=\sqrt{64*521}=\sqrt{64}*\sqrt{521}=8\sqrt{521}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-152)-8\sqrt{521}}{2*-16}=\frac{152-8\sqrt{521}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-152)+8\sqrt{521}}{2*-16}=\frac{152+8\sqrt{521}}{-32}
$