Y=-16t^2+145t+8

Solution for Y=-16t^2+145t+8 equation:

=-16Y^2+145Y+8

We move all terms to the left:

-(-16Y^2+145Y+8)=0

We get rid of parentheses

16Y^2-145Y-8=0

a = 16; b = -145; c = -8;
Δ = b2-4ac
Δ = -1452-4·16·(-8)
Δ = 21537
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:

$\sqrt{\Delta}=\sqrt{21537}=\sqrt{9*2393}=\sqrt{9}*\sqrt{2393}=3\sqrt{2393}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-145)-3\sqrt{2393}}{2*16}=\frac{145-3\sqrt{2393}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-145)+3\sqrt{2393}}{2*16}=\frac{145+3\sqrt{2393}}{32}
$