how do I find all real solutions of this quadratic equation.

Question

w^2 = 3(w - 1)

Answer 1

w^2 = 3(w - 1)
w^2 = 3w - 3
w^2 - 3w + 3 = 0

since it doesn't factor, use the formula
x = (3 ± √(9-4(1)(3))/2
= (3 ± √-3)/2

since the discriminant, the value under the square root, is negative, there are no real solutions to your equation