t=-16t^2-12t+200

Solution for t=-16t^2-12t+200 equation:

t=-16t^2-12t+200

We move all terms to the left:

t-(-16t^2-12t+200)=0

We get rid of parentheses

16t^2+12t+t-200=0

We add all the numbers together, and all the variables

16t^2+13t-200=0

a = 16; b = 13; c = -200;
Δ = b2-4ac
Δ = 132-4·16·(-200)
Δ = 12969
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:

$\sqrt{\Delta}=\sqrt{12969}=\sqrt{9*1441}=\sqrt{9}*\sqrt{1441}=3\sqrt{1441}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-3\sqrt{1441}}{2*16}=\frac{-13-3\sqrt{1441}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+3\sqrt{1441}}{2*16}=\frac{-13+3\sqrt{1441}}{32}
$