x^2-2-4(x^2-2)+4=0

Solution for x^2-2-4(x^2-2)+4=0 equation:

x^2-2-4(x^2-2)+4=0

We add all the numbers together, and all the variables

x^2-4(x^2-2)+2=0

We multiply parentheses

x^2-4x^2+8+2=0

We add all the numbers together, and all the variables

-3x^2+10=0

a = -3; b = 0; c = +10;
Δ = b2-4ac
Δ = 02-4·(-3)·10
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*-3}=\frac{0-2\sqrt{30}}{-6}
=-\frac{2\sqrt{30}}{-6}
=-\frac{\sqrt{30}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*-3}=\frac{0+2\sqrt{30}}{-6}
=\frac{2\sqrt{30}}{-6}
=\frac{\sqrt{30}}{-3}
$