Y=-16x^2+50x+50

Solution for Y=-16x^2+50x+50 equation:

=-16Y^2+50Y+50

We move all terms to the left:

-(-16Y^2+50Y+50)=0

We get rid of parentheses

16Y^2-50Y-50=0

a = 16; b = -50; c = -50;
Δ = b2-4ac
Δ = -502-4·16·(-50)
Δ = 5700
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:

$\sqrt{\Delta}=\sqrt{5700}=\sqrt{100*57}=\sqrt{100}*\sqrt{57}=10\sqrt{57}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{57}}{2*16}=\frac{50-10\sqrt{57}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{57}}{2*16}=\frac{50+10\sqrt{57}}{32}
$