Final answer:
To solve the quadratic equation 3x = 0.5x², rearrange it to the form ax² + bx + c = 0. Use the quadratic formula to find the solutions, which are x = 6 or x = 0.
Step-by-step explanation:
To solve the quadratic equation 3x = 0.5x², we can rearrange it to be in the form ax² + bx + c = 0. In this case, that would be 0.5x² - 3x = 0. Now we can solve for x using the quadratic formula:
x = (-b ± √(b² - 4ac))/(2a)
Substituting the values from our equation into the quadratic formula, we get:
x = (-(-3) ± √((-3)² - 4(0.5)(0)))/(2(0.5))
Simplifying further, we get two possible solutions for x: x = 6 or x = 0.