Solve the equation 3x^2 -4x = x^2 +2

Given the equation :

3x^2 -
4x = x^2 + 2

We need to find x value that satisfies the
equation.

First we will move all terms to the left side so
the right side is 0.

==> 3x^2 -4x -x^2 - 2 =
0

==> 2x^2 -4x -2 =
0

Now we will divide by
2.

==> x^2 - 2x -1 =
0

Now we will use the formula to find the
roots.

==> x1= ( 2 + sqrt(4+4) / 2 = (2+ sqrt8)/2 =
(2+2sqrt2)/2 = 1+sqrt2

==> x2=
(1-sqrt2)

Then the values of x that satisfies the equation
are :

x= { (1+sqrt2) , (1-sqrt2)
}