3-x2=2x2-1

Solution for 3-x2=2x2-1 equation:

3-x2=2x^2-1

We move all terms to the left:

3-x2-(2x^2-1)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2+4=0

a = -3; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-3)·4
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*-3}=\frac{0-4\sqrt{3}}{-6}
=-\frac{4\sqrt{3}}{-6}
=-\frac{2\sqrt{3}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*-3}=\frac{0+4\sqrt{3}}{-6}
=\frac{4\sqrt{3}}{-6}
=\frac{2\sqrt{3}}{-3}
$