Y=12x^2-22

Solution for Y=12x^2-22 equation:

=12Y^2-22

We move all terms to the left:

-(12Y^2-22)=0

We get rid of parentheses

-12Y^2+22=0

a = -12; b = 0; c = +22;
Δ = b2-4ac
Δ = 02-4·(-12)·22
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{66}}{2*-12}=\frac{0-4\sqrt{66}}{-24}
=-\frac{4\sqrt{66}}{-24}
=-\frac{\sqrt{66}}{-6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{66}}{2*-12}=\frac{0+4\sqrt{66}}{-24}
=\frac{4\sqrt{66}}{-24}
=\frac{\sqrt{66}}{-6}
$