How do you solve #3x^2+5x-2=0# using the quadratic formula?

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Answer 1 · 2015-07-25T13:45:40

The solutions are: #color(blue)(x=1/3,x=-2#

The equation #3x^2+5x−2# is of the form #color(blue)(ax^2+bx+c=0#

where:
#a=3, b=5, c=-2#

The Discriminant is given by:
#Delta=b^2-4*a*c#

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

# = 25+24=49#

As #Delta>0# there are two solutions,

The solutions are found using the formula:

#x=(-b+-sqrtDelta)/(2*a)#

As #Delta = 49#, #x = (-(5)+-sqrt(49))/(2*3)= (-5+-7)/6#

#x=(-5-7)/6= color(blue)(-2#

#x=(-5+7)/6=color(blue)(1/3#