# How do you solve 5w^2 - 11w + 10 = 0 using the quadratic formula?

Oct 20, 2015

The solutions are
x=color(blue)((11+sqrt(-79))/10

x=color(blue)((11-sqrt(-79))/10

#### Explanation:

$5 {w}^{2} - 11 w + 10 = 0$

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

$a = 5 , b = - 11 , c = 10$

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

$= {\left(- 11\right)}^{2} - \left(4 \cdot 5 \cdot 10\right)$

$= 121 - 200 = - 79$

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

$x = \frac{- \left(- 11\right) \pm \sqrt{- 79}}{2 \cdot 5} = \frac{11 \pm \sqrt{- 79}}{10}$

The solutions are
x=color(blue)((11+sqrt(-79))/10

x=color(blue)((11-sqrt(-79))/10