6x^2-3=1-3x^2

Solution for 6x^2-3=1-3x^2 equation:

6x^2-3=1-3x^2

We move all terms to the left:

6x^2-3-(1-3x^2)=0

We get rid of parentheses

6x^2+3x^2-1-3=0

We add all the numbers together, and all the variables

9x^2-4=0

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

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*9}=\frac{-12}{18}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*9}=\frac{12}{18}
=2/3
$