To solve the equation, we can start by multiplying both sides of the equation by (x+1) to eliminate the denominator:

căn(5x-4) = 2(x+1)

Next, we can square both sides of the equation to eliminate the square root:

(5x-4) = 4(x+1)^2

Expanding the right side:

5x-4 = 4(x^2 + 2x + 1)

Distributing 4:

5x-4 = 4x^2 + 8x + 4

Rearranging the equation to form a quadratic equation:

4x^2 + 3x - 8 = 0

Now we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 4, b = 3, and c = -8. Plugging these values into the quadratic formula:

x = (-3 ± √(3^2 - 4*4*(-8))) / (2*4)

Simplifying:

x = (-3 ± √(9 + 128)) / 8

x = (-3 ± √137) / 8

Therefore, the solutions to the equation are:

x = (-3 + √137) / 8

x = (-3 - √137) / 8