Let D = discrimination
Rules:
If D > 0, there are 2 real number solutions.
If D = 0, there is only 1 real number solution.
If D < 0, there are 2 imaginary solution.
Given 70w2 - 12w + 1 = 0, b = -12, a = 70 and c = 1.
D = b^2 - 4ac
D = (-12)^2 - 4(70)(1)
D = 144 - 280
D = -136
Our D value is less than 0.
Our case is D < 0.
This means the given quadratic equation has 2 imaginary solutions.
