Y=-16x^2+54

Solution for Y=-16x^2+54 equation:

=-16Y^2+54

We move all terms to the left:

-(-16Y^2+54)=0

We get rid of parentheses

16Y^2-54=0

a = 16; b = 0; c = -54;
Δ = b2-4ac
Δ = 02-4·16·(-54)
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{6}}{2*16}=\frac{0-24\sqrt{6}}{32}
=-\frac{24\sqrt{6}}{32}
=-\frac{3\sqrt{6}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{6}}{2*16}=\frac{0+24\sqrt{6}}{32}
=\frac{24\sqrt{6}}{32}
=\frac{3\sqrt{6}}{4}
$