What is x if 1-square root(13+3x^2)=2x ?

We'll impose constraints of existence of square
root:

13+3x^2 >=
0

Since it is a sum of positive amounts, we'll accept any
value of x as solution of equation.

We'll subtract 2x both
sides:

1 - 2x =
sqrt(13+3x^2)

We'll raise to square to eliminate the square
root:

1 - 4x + 4x^2 =
13+3x^2

We'll move all terms to one side and we'll cmbine
like terms:

x^2 - 4x - 12 =
0

We'll apply quadratic
formula:

x1 =
[4+sqrt(64)]/2

x1 = 6

x2 =
(4-8)/2

x2 =
-2

The solutions of the equation are {-2 ;
6}.