Solve for x 3x^2+6x-5=0

Problem

3*x2+6*x−5=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*x2+b*x+c=0 where a=3 b=6 and c=−5

2. Apply the quadratic formula x=(−b±√(,b2−4*a*c))/(2*a) to find the values of x

3. Substitute the values into the formula:

x=(−6±√(,6−4*(3)*(−5)))/(2*(3))

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

x=(−6±√(,36+60))/6

x=(−6±√(,96))/6

5. Simplify the radical by factoring out the largest perfect square from 96 which is 16

√(,96)=√(,16⋅6)=4√(,6)

6. Substitute the simplified radical back into the equation:

x=(−6±4√(,6))/6

7. Divide each term in the numerator by the denominator to simplify the fraction:

x=−1±(2√(,6))/3

Final Answer

x=−1±(2√(,6))/3

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