Solve for x square root of 4x+2=x^3

$\sqrt{4 x + 2} = x^{3}$

Factor $2$ out of $4 x + 2$ .

Factor $2$ out of $4 x$ .

$\sqrt{2 (2 x) + 2} = x^{3}$

Factor $2$ out of $2$ .

$\sqrt{2 (2 x) + 2 (1)} = x^{3}$

Factor $2$ out of $2 (2 x) + 2 (1)$ .

$\sqrt{2 (2 x + 1)} = x^{3}$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 1.40248001$