Question

What is the solution to 12x=4x2+9?

A. x=23x is equal to 2 thirds
B. x=−23x is equal to negative 2 thirds
C. x=32x is equal to 3 halves
D. x=−32

Answer 1

To solve the equation 12x=4x^2+9, rearrange it and set it equal to zero. Use the quadratic formula to find the solution. The solution is x=3/2.

Step-by-step explanation:

To solve the equation 12x=4x^2+9, we need to rearrange it and set it equal to zero. This gives us the quadratic equation 4x^2-12x+9=0. To solve this equation, we can use the quadratic formula, which states that x=(-b±√(b^2-4ac))/(2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a=4, b=-12, and c=9. So, plugging these values into the quadratic formula, we have:

x=(-(-12)±√((-12)^2-4(4)(9)))/(2(4))

x=(12±√(144-144))/(8)

x=(12±√(0))/(8)

x=(12±0)/(8)

x=12/8

x=3/2

Therefore, the solution to the equation 12x=4x^2+9 is x=3/2.