How do you solve 3x^2 - 12x + 2 = 0?

1 Answer
George C.
May 10, 2017

x = 2+-sqrt(30)/3

Explanation:

The equation:

3x^2-12x+2=0

is in the standard form:

ax^2+bx+c=0

with a=3, b=-12 and c=2

The discriminant Delta of a quadratic is given by the formula:

Delta = b^2-4ac = (color(blue)(-12))^2-4(color(blue)(3))(color(blue)(2)) = 144-24 = 120 = 2^2*30

Since Delta > 0, the given quadratic equation has two Real roots, but since Delta is not a perfect square those roots are irrational.

We can find the roots using the quadratic formula:

x = (-b+-sqrt(b^2-4ac))/(2a)

color(white)(x) = (-b+-sqrt(Delta))/(2a)

color(white)(x) = (12+-sqrt(120))/6

color(white)(x) = (12+-sqrt(2^2*30))/6

color(white)(x) = (12+-2sqrt(30))/6

color(white)(x) = 2+-sqrt(30)/3

That is:

x = 2+sqrt(30)/3" " or " "x = 2-sqrt(30)/3

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