A quadratic equation is an equation involving only non-negative powers of the unknown of degee 2 and less. Any quadratic equation can be written in the form \(\displaystyle ax^2+ bx+ c= 0\) where b and c can be 0 but not a.
Notice the word "can", The equation \(\displaystyle 3x^2- 5x= x^2+ 2x- 3\) is not exactly of that form but by subtracting \(\displaystyle x^2+ 2x- 3\) from both sides we get \(\displaystyle 2x^2- 7x+ 3= 0\) which is so \(\displaystyle 3x^2- 5x= x^2+ 2x- 3\) IS a quadratic equation.
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