Y=36+-4x2

Solution for Y=36+-4x2 equation:

=36+-4Y^2

We move all terms to the left:

-(36+-4Y^2)=0

We use the square of the difference formula

-(36-4Y^2)=0

We get rid of parentheses

4Y^2-36=0

a = 4; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·4·(-36)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*4}=\frac{-24}{8}
=-3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*4}=\frac{24}{8}
=3
$