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The solution by "josgarithmetic" is TOTALLY and ABSOLUTELY W R O N G .
Below find the correct solution.
Let "a" be one solution of the given equation = .
Then the other solution is .
If so, then the given polynomial admits factorization
= = (x-a)*(2x-3a) = .
It means that -k = -5a, 3a^2 = k+2, or (substituting)
= ,
= 0 ---> = = .
1. = = 1 ----> k = 5a = 5;
2. = = = . ----> k = 5a = .
Answer. There are TWO solutions for k: 1) k = 5, and 2) k = .
Solved.
God save you of using the method that "josgarithmetic" uses.