Answer: no real solutions, since the discriminant is \(-120\).

We start with the main method. Use the discriminant to decide how many real roots the quadratic equation has.

Expand and collect terms:

\(5x(x-3)=5x-26\)

\(5x^2-15x=5x-26.\)

So

\(5x^2-20x+26=0.\)

For this quadratic,

\(a=5,\quad b=-20,\quad c=26.\)

The discriminant is

\(b^2-4ac=(-20)^2-4(5)(26).\)

Thus

\(b^2-4ac=400-520=-120.\)

Since the discriminant is negative, the equation has no real solutions.

This completes the solution and gives the required result.