Which equation has the solutions x = 5 + / - 2 the squire root of 7 over 3

If you look at the quadratic formula:

x = (-b±√ (b^2-4ac)) / (2a)

We can say that - b=5, b=-5

If I read it right you had ±2√7 which is equal to ±√28, and we know b=-5 so:

±√ (25-4ac) = ±√28

And since 3=2a, a=1.5 making the above:

±√ (25-6c) = ±√28

25-6c=28

-6c=3

c=-0.5

So a=1.5, b=-5, and c=-0.5 thus

y=1.5x^2-5x-0.5

We can check this by reapplying the quadratic formula to the equation above

x = (5±√ (25-4 (1.5) (-0.5)) / 3

x = (5±√ (25+3)) / 3

x = (5±√28) / 3

x = (5±√ (4*7)) / 3

x = (5±2√7) / 3