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

##### 1 Answer
Aug 10, 2015

The solutions for the equation are:
color(blue)(x=-5/2, x=1

#### Explanation:

2x^2+3x−5=0

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 2 , b = 3 , c = - 5$

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

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

$= 9 + 40$

$= 49$

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

$x = \frac{\left(- 3\right) \pm \sqrt{49}}{2 \cdot 2} = \frac{\left(- 3 \pm 7\right)}{4}$

x = (-3-7)/4, color(blue)(x=-5/2

x=(-3+7)/4, color(blue)(x=1