Question

Which equation has the solutions x= 5 ± 2 square root 7 all over 3

Answer 1

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.

You can see that a=1 (there is just an x²)
b = (-5 -2√7 + 2√7 - 5)/3 = -10/3
c = ((-5-2√7)/3 ) * (-5+2√7)/3) = -1/3

So the equation you're looking for is:

$\frac{3 x^{2} -10x - 1}3 = 0$