Question 6798
The only thing wrong with this question is it should be under quadratic equations.
The solutions you have are correct and can be seen from factoring or using the quadratic equation:

Factoring: {{{(3x^2 -13x -10)=(3x+2)(x-5)}}}
This expression is zero for x=5 and x=-2/3.

The quadratic equation gives: {{{x = (13 +- sqrt( 13^2-4*3*(-10) ))/(2*3) }}} which equals {{{x = (13 +- sqrt(289))/6}}} which equals {{{x=(13 +- 17)/6}}}.
The two answers are 30 / 6 = 5 and -4/6 = -2/3.