15p+15p+25p=30p+25p=55p
(5x+1)(5x+1)=25x+5x+5x+1=35x+1
The area of the square rug is (35x+1).
I may be wrong, I never was good at these types of problems.
ANSWER
No real roots.
The roots are complex or imaginary.
EXPLANATION
The quadratic equation

has discriminant,

If the discriminant is less than zero , then the quadratic equation has no real roots.
The given discriminant is -9.
Since -9 is less than zero, it means the quadratic equation has complex or imaginary roots.