Quadratic equations

Quadratic equation
$$a\cdot x^{2}+b\cdot x+c = 0$$
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Discriminant of a quadratic equation
$$D = b^{2}-4\cdot a\cdot c$$
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Root of a quadratic equation (smaller)
$$x = \frac{-b-\sqrt {D}}{2}$$
D - discriminant
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Root of a quadratic equation (bigger)
$$x = \frac{-b+\sqrt {D}}{2}$$
D - discriminant
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Factorization of quadratic trinomial
$$a\cdot x^{2}+b\cdot x+c = a\cdot (x-x_1)\cdot (x-x_2)$$
x1, x2 - roots of quadratic equation
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separation
$$a\cdot x^{2}+b\cdot x+c = a\cdot (x+\frac{b}{2\cdot a})^{2}+(4\cdot a\cdot c-\frac{b^{2}}{4\cdot a})$$
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