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

Jul 25, 2015

The solutions are: color(blue)(x=1/3,x=-2

#### Explanation:

The equation 3x^2+5x−2 is of the form color(blue)(ax^2+bx+c=0

where:
$a = 3 , b = 5 , c = - 2$

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

$= {\left(5\right)}^{2} - \left(4\right) \cdot \left(3\right) \cdot \left(- 2\right)$

$= 25 + 24 = 49$

As $\Delta > 0$ there are two solutions,

The solutions are found using the formula:

$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

As $\Delta = 49$, $x = \frac{- \left(5\right) \pm \sqrt{49}}{2 \cdot 3} = \frac{- 5 \pm 7}{6}$

x=(-5-7)/6= color(blue)(-2

x=(-5+7)/6=color(blue)(1/3