Y=-16x^2+80x+40

Solution for Y=-16x^2+80x+40 equation:

=-16Y^2+80Y+40

We move all terms to the left:

-(-16Y^2+80Y+40)=0

We get rid of parentheses

16Y^2-80Y-40=0

a = 16; b = -80; c = -40;
Δ = b2-4ac
Δ = -802-4·16·(-40)
Δ = 8960
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:

$\sqrt{\Delta}=\sqrt{8960}=\sqrt{256*35}=\sqrt{256}*\sqrt{35}=16\sqrt{35}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-16\sqrt{35}}{2*16}=\frac{80-16\sqrt{35}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+16\sqrt{35}}{2*16}=\frac{80+16\sqrt{35}}{32}
$