How do you solve x^2 + 5x + 3 = 0?

Aug 2, 2015

The solutions are
color(blue)(x=(-5+sqrt(13))/2 , x=(-5-sqrt(13))/2

Explanation:

The equation ${x}^{2} + 5 x + 3$ is of the form color(blue)(ax^2+bx+c=0 where:
$a = 1 , b = 5 , c = 3$

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

$= {\left(5\right)}^{2} - \left(4 \cdot \left(1\right) \cdot 3\right)$

$= 25 - 12 = 13$

As $\Delta > 0$ there are two solutions,
The solutions are found using the formula
$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

x = (-(5)+-sqrt(13))/(2*1) =color(blue)( (-5+sqrt(13))/2

x = color(blue)((-5-sqrt(13))/2