Answer
No, "$x^{2}=x^{2}+4$" is not a Quadratic equation.
Work Step by Step
Simplifying the giving equation further, we get: "$0=4$", which is not true. There is no way "Zero equals-to Four" or "Four Equals to Zero".
Therefore the equation is not a proper equation and not a quadratic equation either.
The equation doesn't even have the highest exponential term as "x^{2}" too.
