√2x + 3 = x

First, let's isolate the radical on one side:

√2x = x - 3

Next, square both sides of the equation to eliminate the radical:

(√2x)² = (x - 3)²
2x = x² - 6x + 9

Now, move all terms to one side of the equation:

0 = x² - 8x + 9

This is a quadratic equation, so let's solve it by factoring:

0 = (x - 1)(x - 9)

Setting each factor to zero:

x - 1 = 0 or x - 9 = 0
x = 1 or x = 9

Therefore, the solutions to the equation are x = 1 and x = 9.