Y=-162.5t^2+130t+46

Solution for Y=-162.5t^2+130t+46 equation:

=-162.5Y^2+130Y+46

We move all terms to the left:

-(-162.5Y^2+130Y+46)=0

We get rid of parentheses

162.5Y^2-130Y-46=0

a = 162.5; b = -130; c = -46;
Δ = b2-4ac
Δ = -1302-4·162.5·(-46)
Δ = 46800
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:

$\sqrt{\Delta}=\sqrt{46800}=\sqrt{3600*13}=\sqrt{3600}*\sqrt{13}=60\sqrt{13}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-60\sqrt{13}}{2*162.5}=\frac{130-60\sqrt{13}}{325}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+60\sqrt{13}}{2*162.5}=\frac{130+60\sqrt{13}}{325}
$