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

1 Answer
Alan P.
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

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