Question

Can someone help me on this?

Given that 5a^2-4a-13-3(a^2+a+2)=0.What is the sum of the possible values of a?

Answer 1

can be simplified into \[2 a^2-7 a-19\]

Answer 2

When I solve, I get
\[a = 1/4 (7-\sqrt{201})\]
\[a = 1/4 (7+\sqrt{201})\]
add them

Answer 3

just as a short cut, once you have a quadratic polynomial in the form of:
\[x^2+bx+c = 0\]
the sum of the roots is always -b. No need to actually solve for the roots.