# How do you solve 2x^2 - 10x + 7 = 0?

Aug 15, 2015

The solutions are:
color(blue)(x=(5+sqrt(11))/2

color(blue)(x=(5-sqrt(11))/2

#### Explanation:

2x^2−10x+7=0

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 2 , b = - 10 , c = 7$

The Discriminant is given by:

color(blue)(Delta=b^2-4*a*c

$= {\left(- 10\right)}^{2} - \left(4 \cdot 2 \cdot 7\right)$

$= 100 - 56 = 44$

The solutions are found using the formula
color(blue)(x=(-b+-sqrtDelta)/(2*a)

$x = \frac{- \left(- 10\right) \pm \sqrt{44}}{2 \cdot 2} = \frac{10 \pm 2 \sqrt{11}}{4}$

$x = \frac{\cancel{2} \left(5 \pm \sqrt{11}\right)}{\cancel{4}}$

color(blue)(x=(5+sqrt(11))/2

color(blue)(x=(5-sqrt(11))/2