# How do you solve 3x (x - 2) = 1?

Aug 19, 2015

The solutions are
color(blue)(x=(3+2sqrt3)/3
color(blue)(x=(3-2sqrt3)/3

#### Explanation:

3x(x−2)=1

3x^2−6x=1

3x^2−6x-1=0

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 3 , b = - 6 , c = - 1$

The Discriminant is given by:
$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(- 6\right)}^{2} - \left(4 \cdot 3 \cdot \left(- 1\right)\right)$

$= 36 + 12 = 48$

The solutions are found using the formula
$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

$x = \frac{- \left(- 6\right) \pm \sqrt{48}}{2 \cdot 3} = \frac{6 \pm 4 \sqrt{3}}{6}$

$\frac{\cancel{2} \left(3 \pm 2 \sqrt{3}\right)}{\cancel{6}} = \frac{3 \pm 2 \sqrt{3}}{3}$

The solutions are
color(blue)(x=(3+2sqrt3)/3
color(blue)(x=(3-2sqrt3)/3