a)If one root of the equation

x^2 + a(3a-5)x = 2(x+4a) is negative of the other. Find the values of a .

b) If a>0, use the result of (a) to solve the equation.

x^2 + a(3a-5)x = 2(x+4a)

x^2 -2x-8a + +3a^2x - 5ax = 0
x^2 + (3a^2-5a-2)x + 3a^2-8a = 0

since the sum of the roots is -b/a, we have 3a^2-5a-2 = 0.
(3a+1)(a-2) = 0

You can probably take it from here.