<s>[INST] Roots of quadratic equation are given by $b \pm \sqrt{b^2 - c}$ I was reading slides about the cancellation error in quadratic equations and it's written:

The roots of the quadratic equation:
$$x^2 - 2bx + c = 0$$
with $b^2 > c$ are given by $b \pm \sqrt{b^2 - c}$.

Fact that let me perplexed, since I always thought that the roots can be found using the following formula:
$$\frac{b \pm \sqrt{b^2 - 4ac}}{2a}$$
What the relation between one and the other?
 [/INST] Never mind, they can be found by that formula only for this quadratic equation $$x^2 - 2bx + c = 0$$
Indeed if we use the usual formula:
$$\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
to the equation above we obtain:
$$\frac{-(-2b) \pm \sqrt{(-2b)^2 - 4*1*c}}{2*1}$$
$$\frac{2b \pm \sqrt{4b^2 - 4c}}{2}$$
$$\frac{2b \pm \sqrt{4(b^2 - c)}}{2}$$
$$\frac{2b \pm 2\sqrt{b^2 - c}}{2}$$
$$\frac{2(b \pm \sqrt{b^2 - c})}{2}$$
$$b \pm \sqrt{b^2 - c}$$
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