Question 1019659
It is strange to have {{{y}}} on both sides of the equal sign.
If you did post correctly,
{{{y=px^2+8x+p-6y}}}
{{{y+6y=px^2+8x+p}}}
{{{7y=px^2+8x+p}}}<-->{{{y=(px^2+8x+p)/7}}}<-->{{{y=(p/7)x^2+(8/7)x+p/7}}}
If the graph of that quadratic function crosses the {{{y=0}} x-axis,
it will do it at two values of {{{x}}} ,
meaning that {{{y=0}}} will give two distinct solutions for {{{x}}} .
That means {{{px^2+8x+p=0}}} has  two distinct solutions for {{{x}}} .
If a quadratic equation {{{ax^2+bx+c=0}}} has two distinct solutions for {{{x}}} ,
it means that the discriminant is positive:
{{{b^2-4ac>0}}} .
In this case, that would be
{{{8^2-4*p*p>0}}}
{{{64-4p^2>0}}}
{{{16-p^2>0}}}
{{{16>p^2}}}
{{{highlight(-4<p<4)}}}