Solve for x 12x^2-252x+902=0

Problem

12*x2−252*x+902=0

Solution

1. Simplify the equation by dividing all terms by the greatest common divisor, which is 2

6*x2−126*x+451=0

2. Identify the coefficients for the quadratic formula a*x2+b*x+c=0

a=6

b=−126

c=451

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

x=(−(−126)±√(,(−126)2−4*(6)*(451)))/(2*(6))

4. Calculate the discriminant D=b2−4*a*c

D=15876−10824

D=5052

5. Simplify the square root of the discriminant.

√(,5052)=√(,4×1263)

√(,5052)=2√(,1263)

6. Substitute the simplified discriminant back into the formula.

x=(126±2√(,1263))/12

7. Reduce the fraction by dividing the numerator and denominator by 2

x=(63±√(,1263))/6

Final Answer

x=(63±√(,1263))/6

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