Y=200t-16t^2

Solution for Y=200t-16t^2 equation:

=200Y-16Y^2

We move all terms to the left:

-(200Y-16Y^2)=0

We get rid of parentheses

16Y^2-200Y=0

a = 16; b = -200; c = 0;
Δ = b2-4ac
Δ = -2002-4·16·0
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-200}{2*16}=\frac{0}{32}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+200}{2*16}=\frac{400}{32}
=12+1/2
$