Y=9x^2-6

Solution for Y=9x^2-6 equation:

=9Y^2-6

We move all terms to the left:

-(9Y^2-6)=0

We get rid of parentheses

-9Y^2+6=0

a = -9; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-9)·6
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*-9}=\frac{0-6\sqrt{6}}{-18}
=-\frac{6\sqrt{6}}{-18}
=-\frac{\sqrt{6}}{-3}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*-9}=\frac{0+6\sqrt{6}}{-18}
=\frac{6\sqrt{6}}{-18}
=\frac{\sqrt{6}}{-3}
$