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

Problem

3*x2+x−2=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=1

c=−2

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

x=(−(1)±√(,(1)2−4*(3)*(−2)))/(2*(3))

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

x=(−1±√(,1+24))/6

x=(−1±√(,25))/6

4. Evaluate the square root and solve for both possible values of x

x=(−1±5)/6

5. Calculate the first solution using the plus sign.

x=(−1+5)/6=4/6=2/3

6. Calculate the second solution using the minus sign.

x=(−1−5)/6=(−6)/6=−1

Final Answer

x=2/3,−1

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