With parallel lines, ? i know that in order for two lines to be parallel, their slopes must be exactly equal. however, is it true that in order for these lines to be parallel, their slopes must be positive? in advance!

No, in order for the lines to be parallel, the slopes have to be the same, it does not matter what the slopes are as long as they are the same slope. The lines could still be parallel if the slopes are negative.

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0