Y=-16x^2+84x

Solution for Y=-16x^2+84x equation:

=-16Y^2+84Y

We move all terms to the left:

-(-16Y^2+84Y)=0

We get rid of parentheses

16Y^2-84Y=0

a = 16; b = -84; c = 0;
Δ = b2-4ac
Δ = -842-4·16·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-84}{2*16}=\frac{0}{32}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+84}{2*16}=\frac{168}{32}
=5+1/4
$