# How do you solve 6n^2-19n+15=0?

May 19, 2016

The solutions for the expression are:
$n = \frac{5}{3}$

$n = \frac{3}{2}$

#### Explanation:

$6 {n}^{2} - 19 n + 15 = 0$

The equation is of the form color(blue)(an^2+bn+c=0 where:
$a = 6 , b = - 19 , c = 15$

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

$= {\left(- 19\right)}^{2} - \left(4 \cdot 6 \cdot 15\right)$

$= 361 - 360 = 1$

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

$n = \frac{- \left(- 19\right) \pm \sqrt{1}}{2 \cdot 6} = \frac{19 \pm 1}{12}$

$n = \frac{19 + 1}{12} = \frac{20}{12} = \frac{5}{3}$

$n = \frac{19 - 1}{12} = \frac{18}{12} = \frac{3}{2}$