Solve Using the Quadratic Formula 3x^2-8x+4=0

Problem

3*x2−8*x+4=0

Solution

1. Identify the coefficients a b and c from the quadratic equation in the form a*x2+b*x+c=0

a=3

b=−8

c=4

2. State the quadratic formula used to find the roots of the equation.

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the identified values into the quadratic formula.

x=(−(−8)±√(,(−8)2−4*(3)*(4)))/(2*(3))

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

x=(8±√(,64−48))/6

x=(8±√(,16))/6

5. Evaluate the square root and simplify the fraction for both the plus and minus cases.

x=(8±4)/6

6. Solve for the two possible values of x

(x_1)=(8+4)/6=12/6=2

(x_2)=(8−4)/6=4/6=2/3

Final Answer

x=2,2/3

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