Y=512-0,5x^2

Solution for Y=512-0,5x^2 equation:

=512-0.5Y^2

We move all terms to the left:

-(512-0.5Y^2)=0

We get rid of parentheses

0.5Y^2-512=0

a = 0.5; b = 0; c = -512;
Δ = b2-4ac
Δ = 02-4·0.5·(-512)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32}{2*0.5}=\frac{-32}{1}
=-32
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32}{2*0.5}=\frac{32}{1}
=32
$