Y=20-12x^2

Solution for Y=20-12x^2 equation:

=20-12Y^2

We move all terms to the left:

-(20-12Y^2)=0

We get rid of parentheses

12Y^2-20=0

a = 12; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·12·(-20)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*12}=\frac{0-8\sqrt{15}}{24}
=-\frac{8\sqrt{15}}{24}
=-\frac{\sqrt{15}}{3}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*12}=\frac{0+8\sqrt{15}}{24}
=\frac{8\sqrt{15}}{24}
=\frac{\sqrt{15}}{3}
$