Techniques of Differentiation

When $\displaystyle 3x+4\sqrt{x}-1=0$ then why is $\displaystyle \sqrt{x}=\frac{-2+\sqrt{7}}{3}?$

It wouldn't be a problem for me if the equation would be in the normal quadratic form. Multiplying all terms with $\displaystyle x$ wouldn't do any good since I would get $\displaystyle x\sqrt{x}$. Same if I would quadratize the equation by itself.

I think that they used the quadratic formula somehow but I don't see how.

Obviously the problem is the combination of