Y=3x2-24

Solution for Y=3x2-24 equation:

=3Y^2-24

We move all terms to the left:

-(3Y^2-24)=0

We get rid of parentheses

-3Y^2+24=0

a = -3; b = 0; c = +24;
Δ = b2-4ac
Δ = 02-4·(-3)·24
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*-3}=\frac{0-12\sqrt{2}}{-6}
=-\frac{12\sqrt{2}}{-6}
=-\frac{2\sqrt{2}}{-1}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*-3}=\frac{0+12\sqrt{2}}{-6}
=\frac{12\sqrt{2}}{-6}
=\frac{2\sqrt{2}}{-1}
$