To solve the equation 150 : x^2 + 2 + 72 = 84, we need to isolate the variable x.

First, let's simplify the equation:
150 : x^2 + 74 = 84

Next, let's move 74 to the other side of the equation:
150 : x^2 = 84 - 74
150 : x^2 = 10

To get rid of the fraction, we can multiply both sides of the equation by x^2:
150 = 10x^2

Now, divide both sides of the equation by 10:
15 = x^2

Finally, take the square root of both sides to solve for x:
x = ±√15

Therefore, the solutions to the equation are x = √15 and x = -√15.