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

Problem

3*x2−x−4=0

Solution

1. Identify the coefficients a b and c from the standard form a*x2+b*x+c=0

a=3

b=−1

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=(−(−1)±√(,(−1)2−4*(3)*(−4)))/(2*(3))

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

x=(1±√(,1+48))/6

x=(1±√(,49))/6

5. Evaluate the square root.

x=(1±7)/6

6. Solve for the two possible values of x by calculating both the addition and subtraction cases.

(x_1)=(1+7)/6=8/6=4/3

(x_2)=(1−7)/6=(−6)/6=−1

Final Answer

x=4/3,−1

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