Given:
x^2  5x = 1
This can be written as 2 equations:
x^2  5x = 1
x^2  5x  1 = 0  1
x^2  5x = 1
x^2  5x + 1 = 0  2
Solving both quadratic equations would be timeconsuming, and we don’t need the actual value of the roots. Hence, check the value of the discriminant i.e. b^  4ac
For equation 1, we get
5^2  4(1)(1) = 21
For equation 2, we get
5^2  4(1)(1) = 25
When the discriminant is positive, the equation has 2 roots.
Since both equations have positive discriminants, the total number of x values satisfying the equation =
2+2 = 4
Answer: 4
Note: Properties of Discriminants 

A positive discriminant indicates that the quadratic has two distinct real number solutions.

A discriminant of zero indicates that the quadratic has a repeated real number solution.

A negative discriminant indicates that neither of the solutions are real numbers.
[Source: https://www.khanacademy.org/]