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

1 Answer
Alan P.
Jul 8, 2015

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

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