N2004 P1 Q5

The numbers \(x\) and \(y\) satisfy the equation \(4{{x}^{2}}+16xy+{{y}^{2}}+16x+14y+13=0\).

If a real value of \(x\) is substituted, the equation becomes a quadratic equation in \(y\).

Given that two distinct real values of \(y\) may be found from this equation, show that \(5{{x}^{2}}+8x+3>0\), and hence find the set of possible values of \(x\).