Solve Using the Quadratic Formula 2x^2+6x-3=0

Problem

2*x2+6*x−3=0

Solution

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

a=2

b=6

c=−3

2. State the quadratic formula used to find the roots of the equation.

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the identified values into the quadratic formula.

x=(−(6)±√(,(6)2−4*(2)*(−3)))/(2*(2))

4. Simplify the expression inside the square root, which is the discriminant.

x=(−6±√(,36+24))/4

x=(−6±√(,60))/4

5. Simplify the radical by factoring out the largest perfect square.

√(,60)=√(,4⋅15)=2√(,15)

x=(−6±2√(,15))/4

6. Reduce the fraction by dividing the numerator and the denominator by their greatest common factor, which is 2

x=(2*(−3±√(,15)))/4

x=(−3±√(,15))/2

Final Answer

x=(−3±√(,15))/2

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