# How do you solve 7x^2 = 21x using the quadratic formula?

May 17, 2016

#### Answer:

The solutions are:
$x = 3$

$x = 0$

#### Explanation:

$7 {x}^{2} = 21 x$

$7 {x}^{2} - 21 x = 0$

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

$a = 7 , b = - 21 , c = 0$
(the expression has no constant term)

The Discriminant is given by:

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

$= {\left(- 21\right)}^{2} - \left(4 \cdot 7 \cdot 0\right)$

$= 441$

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

$x = \frac{- \left(- 21\right) \pm \sqrt{441}}{2 \cdot 7} = \frac{21 \pm 21}{14}$

$x = \frac{21 + 21}{14} = \frac{42}{14} = 3$

$x = \frac{21 - 21}{14} = \frac{0}{14} = 0$