The given equation is a quadratic equation of the form ax² + bx + c = 0, where a = 3, b = -4 and c = 0.
So, the quadratic equation is 3x² - 4x = 0.
To find the roots of the equation, we could use the quadratic formula, which is given by:
x = [ -b ± sqrt(b² - 4ac) ] / 2a
In our equation, a = 3, b = -4 and c = 0. First, we need to calculate the discriminant, which is part of the quadratic formula. The discriminant is given by b² - 4ac.
For our equation, the discriminant is (-4)² - 4*3*0 = 16.
Since the discriminant is non-negative, we have two real roots for the equation. The roots can be found using the quadratic formula, which gives us:
x₁ = [ -(-4) - sqrt(16) ] / 2*3 = 0
x₂ = [ -(-4) + sqrt(16) ] / 2*3 = 1.3333...
So, the solutions of the equation 3x² - 4x = 0 are x₁ = 0 and x₂ = 1.3333, or in fractional form, 4/3.