Y=20-6x^2

Solution for Y=20-6x^2 equation:

=20-6Y^2

We move all terms to the left:

-(20-6Y^2)=0

We get rid of parentheses

6Y^2-20=0

a = 6; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·6·(-20)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*6}=\frac{0-4\sqrt{30}}{12}
=-\frac{4\sqrt{30}}{12}
=-\frac{\sqrt{30}}{3}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*6}=\frac{0+4\sqrt{30}}{12}
=\frac{4\sqrt{30}}{12}
=\frac{\sqrt{30}}{3}
$