# How do you solve 3x^2+5x=0 using the quadratic formula?

Aug 26, 2015

$x = 0$
or
$x = - \frac{5}{3}$

#### Explanation:

$\textcolor{w h i t e}{\text{XXXX}} a {x}^{2} + b x + c = 0$

Re-writing the given equation in explicit standard form:
$\textcolor{w h i t e}{\text{XXXX}} 3 {x}^{2} + 5 x + 0 = 0$
with $a = 3$, $b = 5$, and $c = 0$

$\textcolor{w h i t e}{\text{XXXX}} x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

which, in this case becomes
color(white)("XXXX")x = (-5+-sqrt(5^2-4(3)(0)))/(2(3)

$\Rightarrow x = 0 \mathmr{and} x = - \frac{10}{6} = - \frac{5}{3}$

Aug 26, 2015

The solutions are

color(blue)(x=0

color(blue)(x=-5/3

#### Explanation:

The equation $3 {x}^{2} + 5 x = 0$:
is of the form color(blue)(ax^2+bx+c=0 where:

$a = 3 , b = 5 , c = 0$
(the equation lacks a constant term)

The Discriminant is given by:
$\Delta = {b}^{2} - 4 \cdot a \cdot c$
$= {\left(5\right)}^{2} - \left(4 \cdot 3 \cdot 0\right)$
$= 25 - 0 = 25$

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

$x = \frac{\left(- 5\right) \pm \sqrt{25}}{2 \cdot 3} = \frac{\left(- 5 \pm 5\right)}{6}$

x=((-5+5))/6, color(blue)(x=0

x=((-5-5))/6, x=-10/6 color(blue)(x=-5/3