For what values of m are the roots of the quadratic equation mx (x - 2√5) + 10 = 0 real and equal?

Question: For what values of m are the roots of the quadratic equation mx (x - 2√5) + 10 = 0 real and equal?

Solution:
mx (x - 2√5) + 10 = 0
⇒ mx² - 2√5 mx + 10 = 0

Compare the given equation with the general form of the quadratic equation, which ax² + bx + c = 0
a = m, b = - 2√5m, c = 10

Since roots are real and equal, discriminant, D = 0
b² - 4ac = 0
⇒ (- 2√5m)² - 4 × m × 10 = 0
⇒ 20m² - 40m = 0
⇒ 20(m² - 2m) = 0
⇒ m² - 2m = 0
⇒ m(m - 2) = 0

Either, m = 0

Or, m - 2 = 0
∴ m = 2