determine what type of number the solutions are and how many solutions exist

5x^2=48x

5x^2 = 48x

5x^2 - 48x = 0
x(5x - 48) = 0
therefore,
x = 0 and x = 48/5
there are two solutions, and they are both real numbers.

hope this helps~ :)

To determine the type and number of solutions for the equation 5x^2 = 48x, we need to solve it and analyze the results.

Step 1: Rewrite the equation in standard form
To set the equation equal to zero, we'll subtract 48x from both sides:
5x^2 - 48x = 0

Step 2: Factor out common terms if possible
In this case, we can factor out an x:
x(5x - 48) = 0

Step 3: Apply the zero-product property
The zero-product property states that if a product of factors is equal to zero, then at least one of the factors must be zero.
Therefore, we set each factor equal to zero and solve for x:

x = 0 (Equation 1)
5x - 48 = 0 (Equation 2)

Solving Equation 2 for x:
5x = 48
x = 48/5
x = 9.6

Step 4: Analyze the solutions
Now that we have the solutions, we can determine their type and quantity.

In this case, we have two solutions: x = 0 and x = 9.6.
- x = 0 is a real number solution.
- x = 9.6 is also a real number solution.

Therefore, the solutions to the equation 5x^2 = 48x are both real numbers, and there are two solutions.