We can take the square root of both sides, adding a plus/minus sign of the right hand side:
[tex]\sqrt{(y+150)^2}=\pm\sqrt{50}\iff y+150 = \pm\sqrt{50}[/tex]
Then, we subtract 150 from both sides:
[tex]y=\pm\sqrt{50}-150[/tex]
So, the two solutions are
[tex]y_1 = \sqrt{50}-150,\quad y_2 = -\sqrt{50}-150[/tex]
