Question 21992
Well, hang in there "old man"! (I'm 73!)
First, let's find the solutions or roots, as they are commonly called.

{{{3x^2 + 11x = 4}}} First subtract 4 from both sides of the equation.
{{{3x^2 + 11x - 4 = 0}}} Solve this quadratic equation by factoring.
{{{(3x - 1)(x + 4) = 0}}} Now apply the zero product principle.
{{{(3x - 1) = 0}}} and/or {{{(x + 4) = 0}}}
If {{{3x - 1 = 0}}} then, {{{3x = 1}}} and {{{x = 1/3}}}
If {{{x + 4 = 0}}} then, {{{x = -4}}}

The roots are:
{{{x = 1/3}}}
{{{x = -4}}}
 So their sum is:
{{{1/3 - 4}}} = -3 1/3 

Your daughter is correct!