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The following equations are quadratic: $$\Tred{x^2}-1 = 0, \quad 3\Tred{t^2} + 2\Tred{t} + 1 = -2.$$
The following equations are not quadratic: $$\Tred{x}^3 = 1,\quad \sqrt{\Tred{t}} - 1 = 0,\quad \frac{1}{\Tred{y}+1} + \frac{1}{\Tred{y}} + \frac{1}{\Tred{y}-1} = 1$$
The general form of a quadratic equation is $$\Tblue{a} \Tred{x}^2 + \Tblue{b}\Tred{x} + \Tblue{c} = 0$$ for numbers $\Tblue{a}\ne0$, $\Tblue{b}$ and $\Tblue{c}$.