Solve Using the Quadratic Formula 4x^2+9=12x

Problem

4*x2+9=12*x

Solution

1. Rearrange the equation into standard form a*x2+b*x+c=0 by subtracting 12*x from both sides.

4*x2−12*x+9=0

2. Identify the coefficients a b and c for the quadratic formula.

a=4

b=−12

c=9

3. Substitute these values into the quadratic formula x=(−b±√(,b2−4*a*c))/(2*a)

x=(−(−12)±√(,(−12)2−4*(4)*(9)))/(2*(4))

4. Simplify the expression inside the square root (the discriminant).

x=(12±√(,144−144))/8

5. Evaluate the square root and solve for x

x=(12±√(,0))/8

x=12/8

6. Reduce the fraction to its simplest form.

x=3/2

Final Answer

x=3/2

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