(12y^2-144)=3y^2

Solution for (12y^2-144)=3y^2 equation:

(12y^2-144)=3y^2

We move all terms to the left:

(12y^2-144)-(3y^2)=0

determiningTheFunctionDomain
-3y^2+(12y^2-144)=0

We get rid of parentheses

-3y^2+12y^2-144=0

We add all the numbers together, and all the variables

9y^2-144=0

a = 9; b = 0; c = -144;
Δ = b2-4ac
Δ = 02-4·9·(-144)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72}{2*9}=\frac{-72}{18}
=-4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72}{2*9}=\frac{72}{18}
=4
$