To solve the equation √2x+1+√8x+4=6, we can start by isolating one of the square root terms on one side of the equation.

√2x+1 = 6 - √8x+4

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

(√2x+1)^2 = (6 - √8x+4)^2

Simplifying the left side:

2x + 1 = (6 - √8x+4)(6 - √8x+4)

Expanding the right side:

2x + 1 = 36 - 6√8x+4 - 6√8x+4 + 8x + 4

Combining like terms:

2x + 1 = 40 - 12√8x+4 + 8x

Rearranging the terms:

2x - 8x = 40 - 1 - 12√8x+4

-6x = 39 - 12√8x+4

Dividing both sides by -6:

x = (39 - 12√8x+4) / -6

Simplifying further:

x = -6.5 + 2√8x+4

This equation cannot be easily solved algebraically. However, you can use numerical methods or approximation techniques to find an approximate solution for x.