# How do you solve the equation: x^2 + 7x - 3 = 0?

Jul 6, 2015

The solutions are:
x = color(blue)( (-7+sqrt(61))/(2

 x =color(blue)( (-7-sqrt(61))/(2

#### Explanation:

${x}^{2} + 7 x - 3 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 1 , b = 7 , c = - 3$

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

 = (7)^2-(4*(1)*(-3)

$= 49 + 12 = 61$

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

x = ((-7)+-sqrt(61))/(2*1) = ((-7)+-sqrt(61))/(2
The solutions are:
x = color(blue)( (-7+sqrt(61))/(2

 x =color(blue)( (-7-sqrt(61))/(2