Solve Using the Quadratic Formula 3x^2+18x+15=0

Problem

3*x2+18*x+15=0

Solution

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

a=3

b=18

c=15

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=(−18±√(,18−4*(3)*(15)))/(2*(3))

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

x=(−18±√(,324−180))/6

x=(−18±√(,144))/6

5. Evaluate the square root and simplify the fraction.

x=(−18±12)/6

6. Solve for both possible values of x by calculating the plus and minus cases.

(x_1)=(−18+12)/6=(−6)/6=−1

(x_2)=(−18−12)/6=(−30)/6=−5

Final Answer

x=−1,−5

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