Question

What is the solution set of `4/5x^2 = 2x- 4/5`?

Answer 1

`x in {1/2,2}`

Explanation:

Given
`color(white)("XXX")4/5x^2=2x-4/5`

Multiplying everything by `5`
`color(white)("XXX")4x^2=10x-4`

Divide everything by `2`
`color(white)("XXX")2x^2=5x-2`

Re-arrange in standard form:
`color(white)("XXX")2x^2-5x+2 = 0`

Factor (use the quadratic formula if necessary)
`color(white)("XXX")(2x-1)(x-2)=0`

So
`color(white)("XXX")2x-1=0 rarr color(green)(x=1/2)`
or
`color(white)("XXX")x-2=0 rarr color(green)(x=2)`