Y=-32t^2+130t

Solution for Y=-32t^2+130t equation:

=-32Y^2+130Y

We move all terms to the left:

-(-32Y^2+130Y)=0

We get rid of parentheses

32Y^2-130Y=0

a = 32; b = -130; c = 0;
Δ = b2-4ac
Δ = -1302-4·32·0
Δ = 16900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16900}=130$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-130}{2*32}=\frac{0}{64}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+130}{2*32}=\frac{260}{64}
=4+1/16
$