Y=16(-t^2+9t+16)

Solution for Y=16(-t^2+9t+16) equation:

=16(-Y^2+9Y+16)

We move all terms to the left:

-(16(-Y^2+9Y+16))=0


We calculate terms in parentheses: -(16(-Y^2+9Y+16)), so:

16(-Y^2+9Y+16)

We multiply parentheses

-16Y^2+144Y+256

Back to the equation:

-(-16Y^2+144Y+256)


We get rid of parentheses

16Y^2-144Y-256=0

a = 16; b = -144; c = -256;
Δ = b2-4ac
Δ = -1442-4·16·(-256)
Δ = 37120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{37120}=\sqrt{256*145}=\sqrt{256}*\sqrt{145}=16\sqrt{145}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-16\sqrt{145}}{2*16}=\frac{144-16\sqrt{145}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+16\sqrt{145}}{2*16}=\frac{144+16\sqrt{145}}{32}
$