Simple equation with square root $2x-6-4\sqrt x=0$

Question

Good evening to everybody, I have a doubt about the following simple equation:

$$2x-6-4\sqrt x=0$$

I know that x should equal to $9$.

But how do I arrive to this result? In particular, my difficulty is to deal with square root. Thanks in advance!

Answer 1

HINT

Let $\sqrt x = t\ge 0$ then we have

$$2x-6-4\sqrt x=0 \iff 2t^2-4t-6=0$$

then solve the quadratic equation and then select the solutions $t\ge 0$.

Answer 2

$x>0.$

$x-3-2\sqrt x=0.$

$(√x+1)(√x -3)=0$.

The only solution is $√x=3$ (why?).