Solve for x 12x^2-120x+209=0

Problem

12*x2−120*x+209=0

Solution

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

a=12

b=−120

c=209

2. Apply the quadratic formula to find the values of x

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values of a b and c into the formula.

x=(−(−120)±√(,(−120)2−4*(12)*(209)))/(2*(12))

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

x=(120±√(,14400−10032))/24

x=(120±√(,4368))/24

5. Simplify the radical by finding the largest perfect square factor of 4368

4368=16×273

√(,4368)=4√(,273)

6. Substitute the simplified radical back into the equation.

x=(120±4√(,273))/24

7. Divide each term in the numerator by the denominator to simplify the fraction.

x=120/24±(4√(,273))/24

x=5±√(,273)/6

Final Answer

x=5±√(,273)/6

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