How to solve 2 x 2 - 2 = 6 ?

First, to isolate the ${\displaystyle x^2}$ term and maintain the equation's balance, add ${\displaystyle 2}$ to each side of the equation:
${\displaystyle 2x^2-2+2=6+2}$
${\displaystyle 2x^2-0=8}$
${\displaystyle 2x^2=8}$
Next, divide each side of the equation by ${\displaystyle 2}$ to isolate ${\displaystyle x^2}$ while keeping the equation balanced:
${\displaystyle \frac{2x^2}{2}=\frac{8}{2}}$
${\displaystyle \frac{\cancel{2}{x}^2}{\cancel{2}}=4}$
${\displaystyle x^2=4}$
To solve for ${\displaystyle x}$ while keeping the equation balanced, take the square root of each side of the equation. Remember that there are two solutions—one negative and one positive—when computing the square root of a number:
${\displaystyle \sqrt{x^2}=\pm \sqrt{4}}$
${\displaystyle x=\pm \sqrt{4}=\pm 2}$