Obviously,
X = 4
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what is x^2 + x = x^2 + 4?
Depending on how facile you are with algebra, it may or not be obvious to you---nor should it be.
The general rule is that you can add, subtract, multiply, and divide the both sides of an equation by the same amount and not change the "truth" (equality) of the original equation.
So add a (-x^2) to each side, and you have your answer.
John gave you an answer and a put-down.
I reminded you how to solve it.
x^2 + x = x^2 + 4
subtract x^2 from both sides-
x^2 - x^2 + x = x^2 - x^2 + 4
0 + x = 0 + 4
x = 4
