Solve Using the Quadratic Formula 3x^2+10x-8=0

Problem

3*x2+10*x−8=0

Solution

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

a=3

b=10

c=−8

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=(−10±√(,10−4*(3)*(−8)))/(2*(3))

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

x=(−10±√(,100+96))/6

x=(−10±√(,196))/6

5. Evaluate the square root.

x=(−10±14)/6

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

(x_1)=(−10+14)/6=4/6=2/3

(x_2)=(−10−14)/6=(−24)/6=−4

Final Answer

x=2/3,−4

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