Solve Using the Quadratic Formula 6x^2-x-5=0

Problem

6*x2−x−5=0

Solution

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

a=6

b=−1

c=−5

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*(6)*(−5)))/(2*(6))

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

x=(1±√(,1+120))/12

x=(1±√(,121))/12

5. Evaluate the square root and split the expression into two possible solutions.

x=(1±11)/12

6. Calculate the first solution using the plus sign.

x=(1+11)/12

x=12/12

x=1

7. Calculate the second solution using the minus sign.

x=(1−11)/12

x=(−10)/12

x=−5/6

Final Answer

x=1,−5/6

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