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

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Answer 1 · 2015-08-02T06:13:27

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

The equation #x^2+5x+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*a*c#

# = (5)^2-(4*(1)*3)#

# = 25-12=13#

As #Delta>0# there are two solutions,
The solutions are found using the formula
#x=(-b+-sqrtDelta)/(2*a)#

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

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