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

1 Answer
Jul 6, 2015

Answer:

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

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

Explanation:

#x^2+7x-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*a*c#

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

# = 49 +12=61#

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