Question

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

Answer 1

`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`