# How do you solve 12x^2 - 7x + 1 = 0 ?

Mar 31, 2016

The solutions are:

color(green)(x= 1/3

color(green)(x= 1/4

#### Explanation:

$12 {x}^{2} - 7 x + 1 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 12 , b = - 7 , c = 1$

The Discriminant is given by:

$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(- 7\right)}^{2} - \left(4 \cdot 12 \cdot 1\right)$

$= 49 - 48 = 1$

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

$x = \frac{- \left(- 7\right) \pm \sqrt{1}}{2 \cdot 12} = \frac{7 \pm 1}{24}$

$x = \frac{7 + 1}{24} = \frac{8}{24} = \frac{1}{3}$

$x = \frac{7 - 1}{24} = \frac{6}{24} = \frac{1}{4}$