How to solve #2x-1/3 = x^2+(2x)/5# using the quadratic formula?

1 Answer
Feb 18, 2016

#x~~0.246# or #x~~1.354#

Explanation:

Given
#color(white)("XXX")2x-1/3=x^2+(2x)/5#

This will be easier to work with if we clear the fractions by multiplying everything by #15#
#color(white)("XXX")30x-5=15x^2+6x#
then rearrange into standard form:
#color(white)("XXX")15x^2-24x+5=0#

Now that it is in standard form: #ax^2+bx+c=0#
we can apply the quadratic formula: #x=(-b+-sqrt(b^2-4ac))/(2a)#

#x=(24+-sqrt(24^2-4(15)(5)))/(2(15))#

(with the aid of a calculator)
#color(white)("XXX")=(24+-sqrt(276))/(30)#

#x~~ 0.246# or #x ~~ 1.354#