Solve Using the Quadratic Formula 3x^2+11x-4=0

Problem

3*x2+11*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=11

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 values of a b and c into the formula.

x=(−11±√(,11−4*(3)*(−4)))/(2*(3))

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

x=(−11±√(,121+48))/6

x=(−11±√(,169))/6

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

x=(−11±13)/6

6. Calculate the first solution using the plus sign.

x=(−11+13)/6=2/6=1/3

7. Calculate the second solution using the minus sign.

x=(−11−13)/6=(−24)/6=−4

Final Answer

x=1/3,−4

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