How do you use the quadratic formula to find both solutions to the quadratic equation #3x^2 + 4x = 6#?

1 Answer
Jul 8, 2015

Answer:

#x= (sqrt(22)-2)/3#
or
#x= -(sqrt(22)+2)/3#

Explanation:

#3x^2+4x=6#
is equivalent to
#color(white)("XXXX")##3x^2+4x-6=0#

which is in the standard form
#color(white)("XXXX")##x^2+bx+c=0#
with roots based on the quadratic formula at
#color(white)("XXXX")##x=(-b+-sqrt(b^2-4ac))/(2a)#

with #a=3#, #b=4#, and #c=-6# (from above)

this becomes
#color(white)("XXXX")##x = (-4+-sqrt(4^2-4(3)(-6)))/(2(3)#

#color(white)("XXXX")##x= (-4+-sqrt(16+72))/6#

#color(white)("XXXX")##x= (-2+-sqrt(22))/3#