Y=-16t^2+35t+6

Solution for Y=-16t^2+35t+6 equation:

=-16Y^2+35Y+6

We move all terms to the left:

-(-16Y^2+35Y+6)=0

We get rid of parentheses

16Y^2-35Y-6=0

a = 16; b = -35; c = -6;
Δ = b2-4ac
Δ = -352-4·16·(-6)
Δ = 1609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-\sqrt{1609}}{2*16}=\frac{35-\sqrt{1609}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1609}}{2*16}=\frac{35+\sqrt{1609}}{32}
$