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Those who use this formula really ought to take a few minutes to prove it sometime...
You simply substitute <math>a</math>, <math>b</math>, and <math>c</math> in the formula.
You simply substitute <math>a</math>, <math>b</math>, and <math>c</math> in the formula.
You can prove that the formula is correct by substituting the formula in place of '''x''' in <math>ax^2+bx+c=0\!</math> and then gradually simplying the rather complicated formula that results, step by step. Eventually, if all the simplication steps are done correctly, it will simply to 0.