# How do you solve x^2 + 3x -10 =0 using the quadratic formula?

Mar 25, 2016

The solutions are:
$x = 2$

$x = - 5$

#### Explanation:

${x}^{2} + 3 x - 10 = 0$

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

$a = 1 , b = 3 , c = - 10$

The Discriminant is given by:

color(blue)(Delta=b^2-4*a*c

$= {\left(3\right)}^{2} - \left(4 \cdot 1 \cdot \left(- 10\right)\right)$

$= 9 + 40 = 49$

The solutions are found using the formula
color(blue)(x=(-b+-sqrtDelta)/(2*a)

$x = \frac{\left(- 3\right) \pm \sqrt{49}}{2 \cdot 1} = \frac{- 3 \pm 7}{2}$

$x = \frac{- 3 + 7}{2} = \frac{4}{2} = 2$

$x = \frac{- 3 - 7}{2} = - \frac{10}{2} = - 5$