Let's use the quadratic formula:
2w² - 20w + 50 = 0
a = 2 b = -20 c = 50
x = -b +-sq root(b^2 - 4*a*c) / 2*a
x = --20 +-sq root(400 -4*2*50) / 4
x = 20 +-sq root(400 -4*2*50) / 4
x = 20 +-sq root( 0) / 4
x = 20 / 4 =5
I'd say it has one rational solution.
It does NOT have 2 solutions because the "plus / minus" section = 0.
