Y=-16t^2+37t-20

Solution for Y=-16t^2+37t-20 equation:

=-16Y^2+37Y-20

We move all terms to the left:

-(-16Y^2+37Y-20)=0

We get rid of parentheses

16Y^2-37Y+20=0

a = 16; b = -37; c = +20;
Δ = b2-4ac
Δ = -372-4·16·20
Δ = 89
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{-(-37)-\sqrt{89}}{2*16}=\frac{37-\sqrt{89}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{89}}{2*16}=\frac{37+\sqrt{89}}{32}
$