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what x's make y real?

Source:

March 25, 2006
quadraticsalgebraquadratic formula

Problem Statement

If xx is a real and 4y2+4xy+x+6=04y^2+4xy+x+6=0, then the complete set of values of xx for which yy is real, is:
(A) x≤−2 or x≥3(B) x≤2 or x≥3(C) x≤−3 or x≥2\text{(A)} \ x\le -2~\text{or}~x\ge3 \qquad \text{(B)} \ x\le 2~\text{or}~x\ge3 \qquad \text{(C)} \ x\le -3 ~\text{or}~x\ge 2 \text{(D)} \ -3\le x \le 2\qquad \text{(E)} \ \-2\le x \le 3
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