((3x)^2)-13=(3-(x)^2)

Solution for ((3x)^2)-13=(3-(x)^2) equation:

((3x)^2)-13=(3-(x)^2)

We move all terms to the left:

((3x)^2)-13-((3-(x)^2))=0

determiningTheFunctionDomain
-((3-x^2))+3x^2-13=0

We add all the numbers together, and all the variables

3x^2-((3-x^2))-13=0


We calculate terms in parentheses: -((3-x^2)), so:

(3-x^2)

We get rid of parentheses

-x^2+3

We add all the numbers together, and all the variables

-1x^2+3

Back to the equation:

-(-1x^2+3)


We get rid of parentheses

3x^2+1x^2-3-13=0

We add all the numbers together, and all the variables

4x^2-16=0

a = 4; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·4·(-16)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16}{2*4}=\frac{-16}{8}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16}{2*4}=\frac{16}{8}
=2
$