Here's the graph of both sides......https://www.desmos.com/calculator/omgitpgty8
Notice that there aren't any points of intersection.......thus...no real solutions...
(x - 5x + 12)2 + 1 = -|x| ---> is equivalent to ---> (x - 5x + 12)2 + 1 + |x| = 0
(x - 5x + 12)2 can never be less than 0; similarly |x| can never be less than 0; whatever the sum of these two are, when you add another +1, you must get a number which is greater than 0.
Therefore, there can be no real solutions.
Here's the graph of both sides......https://www.desmos.com/calculator/omgitpgty8
Notice that there aren't any points of intersection.......thus...no real solutions...