Question 858686
{{{x^2+p+x=3(x+1)}}}
x^2 + p + x = 3x + 3
add -3x -3 to each side
x^2 -2x -3 + p
Determine whether roots are real by
seeing if {{{(b^2 -4ac)>=0}}} where
a = 1 , b = -2 , c = ( -3 + p)
{{{(4 - 4(1)(-3 + p) )}}}
{{{(4 - 4(-3 + p) )}}}
{{{(4 + 12 - 4p )}}}
{{{(- 4p + 16 )}}}
When - 4p + 16 > 0 we have real roots
add -16 to each side
 -4p > -16
divide each side by -4
 p < 4