Y=6x^2-54

Solution for Y=6x^2-54 equation:

=6Y^2-54

We move all terms to the left:

-(6Y^2-54)=0

We get rid of parentheses

-6Y^2+54=0

a = -6; b = 0; c = +54;
Δ = b2-4ac
Δ = 02-4·(-6)·54
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36}{2*-6}=\frac{-36}{-12}
=+3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36}{2*-6}=\frac{36}{-12}
=-3
$