Solve for x 3x^2-2x-6=0

Problem

3*x2−2*x−6=0

Solution

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

a=3

b=−2

c=−6

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=(−(−2)±√(,(−2)2−4*(3)*(−6)))/(2*(3))

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

x=(2±√(,4+72))/6

x=(2±√(,76))/6

5. Simplify the radical by factoring out the largest perfect square.

x=(2±√(,4⋅19))/6

x=(2±2√(,19))/6

6. Divide the numerator and denominator by their greatest common factor, which is 2

x=(1±√(,19))/3

Final Answer

x=(1±√(,19))/3

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