How do you solve 7R^2 -14R + 10 = 0 using the quadratic formula?

Oct 25, 2015

The solutions are
color(blue)(x= (14+sqrt(-84))/14

color(blue)(x= (14-sqrt(-84))/14

Explanation:

$7 {R}^{2} - 14 R + 10 = 0$

The equation is of the form color(blue)(aR^2+bR+c=0 where:

$a = 7 , b = - 14 , c = 10$

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

$= {\left(- 14\right)}^{2} - \left(4 \cdot 7 \cdot 10\right)$

$= 196 - 280 = - 84$

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

$x = \frac{- \left(- 14\right) \pm \sqrt{- 84}}{2 \cdot 7} = \frac{14 \pm \sqrt{- 84}}{14}$

The solutions are
color(blue)(x= (14+sqrt(-84))/14

color(blue)(x= (14-sqrt(-84))/14