I am getting conflicting answers...?

Question

Find the sum of the values satisfying the mean value theorem of f(x)=((x^3)/3)-(2x^2)+3x+4 where x is [0,4].

Answer 1

f(0) = 4
f(4) = 16/3
f'(x) = x^2-4x+3 = (16/3 - 4)/4 = 1/3
3x^2-12x+8 = 0
Use quadratic formula to find x.

Answer 2

you don´t need to solve the equation as you are asked for the sum which is
x1+x2 = -b/a if the equation is ax^2 +bx+c=0