Y(t)=16t+-16t2

Solution for Y(t)=16t+-16t2 equation:

(Y)=16Y+-16Y^2

We move all terms to the left:

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

We use the square of the difference formula

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

We get rid of parentheses

16Y^2-16Y+Y=0

We add all the numbers together, and all the variables

16Y^2-15Y=0

a = 16; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·16·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*16}=\frac{0}{32}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*16}=\frac{30}{32}
=15/16
$