4x^2-2x-2=x^2

Solution for 4x^2-2x-2=x^2 equation:

4x^2-2x-2=x^2

We move all terms to the left:

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

determiningTheFunctionDomain
4x^2-x^2-2x-2=0

We add all the numbers together, and all the variables

3x^2-2x-2=0

a = 3; b = -2; c = -2;
Δ = b2-4ac
Δ = -22-4·3·(-2)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{7}}{2*3}=\frac{2-2\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{7}}{2*3}=\frac{2+2\sqrt{7}}{6}
$