To be fair though, it should also be noted that when you distributed the -4 early on in the problem, you ended up with -4x-12....... And should have had -4x+12. Had you done that, then your determinant most likely would have had imaginary solutions.
Rethink this problem a bit. x^2-4x-12= (x+2)(x-6).... These are real root situation. x=-2 and x=6....... They are NOT imaginary. Where your quadric equation went wrong was in the determinant. INSIDE THE DETERMINANT: Think of it this way ----------> 16 take away (4*1*(-12))...... or 16-(-48)=64. Your actually taking the negative away when done correctly. That makes it positive. The determinant is the sq of 64, which equals 8. (4, plus or minus 8)/2...... Which simplifies to 2, plus or minus 4. Result x=6 and x=-2
To be fair though, it should also be noted that when you distributed the -4 early on in the problem, you ended up with -4x-12....... And should have had -4x+12. Had you done that, then your determinant most likely would have had imaginary solutions.
Rethink this problem a bit.
x^2-4x-12= (x+2)(x-6).... These are real root situation. x=-2 and x=6....... They are NOT imaginary.
Where your quadric equation went wrong was in the determinant.
INSIDE THE DETERMINANT:
Think of it this way ----------> 16 take away (4*1*(-12))...... or 16-(-48)=64.
Your actually taking the negative away when done correctly. That makes it positive.
The determinant is the sq of 64, which equals 8.
(4, plus or minus 8)/2...... Which simplifies to 2, plus or minus 4. Result x=6 and x=-2
Two wrongs makes it right