Question

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

Answer 1

`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`