Y=23-3x2

Solution for Y=23-3x2 equation:

=23-3Y^2

We move all terms to the left:

-(23-3Y^2)=0

We get rid of parentheses

3Y^2-23=0

a = 3; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·3·(-23)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{69}}{2*3}=\frac{0-2\sqrt{69}}{6}
=-\frac{2\sqrt{69}}{6}
=-\frac{\sqrt{69}}{3}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{69}}{2*3}=\frac{0+2\sqrt{69}}{6}
=\frac{2\sqrt{69}}{6}
=\frac{\sqrt{69}}{3}
$