-2*x+5*sqrt(x)-2=0 equation

Given the equation
$$\left(5 \sqrt{x} - 2 x\right) - 2 = 0$$
$$5 \sqrt{x} = 2 x + 2$$
We raise the equation sides to 2-th degree
$$25 x = \left(2 x + 2\right)^{2}$$
$$25 x = 4 x^{2} + 8 x + 4$$
Transfer the right side of the equation left part with negative sign
$$- 4 x^{2} + 17 x - 4 = 0$$
This equation is of the form

a*x^2 + b*x + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = -4$$
$$b = 17$$
$$c = -4$$
, then

D = b^2 - 4 * a * c = 

(17)^2 - 4 * (-4) * (-4) = 225

Because D > 0, then the equation has two roots.

x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
$$x_{1} = \frac{1}{4}$$
$$x_{2} = 4$$

Because
$$\sqrt{x} = \frac{2 x}{5} + \frac{2}{5}$$
and
$$\sqrt{x} \geq 0$$
then
$$\frac{2 x}{5} + \frac{2}{5} \geq 0$$
or
$$-1 \leq x$$
$$x < \infty$$
The final answer:
$$x_{1} = \frac{1}{4}$$
$$x_{2} = 4$$