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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -((12y^2-144)), so:

(12y^2-144)

We get rid of parentheses

12y^2-144

Back to the equation:

-(12y^2-144)


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
$