Y=16t^2+72t+5

Solution for Y=16t^2+72t+5 equation:

=16Y^2+72Y+5

We move all terms to the left:

-(16Y^2+72Y+5)=0

We get rid of parentheses

-16Y^2-72Y-5=0

a = -16; b = -72; c = -5;
Δ = b2-4ac
Δ = -722-4·(-16)·(-5)
Δ = 4864
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:

$\sqrt{\Delta}=\sqrt{4864}=\sqrt{256*19}=\sqrt{256}*\sqrt{19}=16\sqrt{19}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-16\sqrt{19}}{2*-16}=\frac{72-16\sqrt{19}}{-32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+16\sqrt{19}}{2*-16}=\frac{72+16\sqrt{19}}{-32}
$