What are the solutions to the quadratic equation 6x² + 24x = 0?

An equation in the form of ax² + bx + c = 0 is a quadratic equation when a ≠ 0. 

Answer: The solutions are 0 and - 4 for equation 6x² + 24x = 0.

Let's solve step by step to find the solutions to the quadratic equation 6x² + 24x = 0.

Explanation:

Given that  6x² + 24x = 0

The quadratic formula is given by x = (- b ± √ b² + 4ac) / 2

As we know that coefficient of x²  is a, coefficient of x is b and constant term is c, so, a = 6, b = 24 and c = 0.

Using the quadratic formula, we get,

⇒ - 24 ± √ (24)² + 4 ( 6 ) 0 / 2 (6) 

⇒ - 24 ± √576  / 12

We can have two values of 'x' when we find square root.

⇒ x = - 24 + √576  / 12 or  x = - 24 - √576 / 12

⇒ x = (- 24 + 24) / 12 or x = (- 24 - 24) / 12 

⇒ x =  0 / 12 or x = - 48 / 12

⇒ x = 0 or - 4

Thus, the solutions are 0 and - 4 for equation 6x² + 24x = 0.