Y=-16x^2+3x+80

Solution for Y=-16x^2+3x+80 equation:

=-16Y^2+3Y+80

We move all terms to the left:

-(-16Y^2+3Y+80)=0

We get rid of parentheses

16Y^2-3Y-80=0

a = 16; b = -3; c = -80;
Δ = b2-4ac
Δ = -32-4·16·(-80)
Δ = 5129
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{-(-3)-\sqrt{5129}}{2*16}=\frac{3-\sqrt{5129}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{5129}}{2*16}=\frac{3+\sqrt{5129}}{32}
$