Solve Using the Quadratic Formula 2x^2+3x-20=0

Problem

2*x2+3*x−20=0

Solution

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

a=2

b=3

c=−20

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=(−(3)±√(,(3)2−4*(2)*(−20)))/(2*(2))

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

x=(−3±√(,9+160))/4

x=(−3±√(,169))/4

5. Evaluate the square root of 169

x=(−3±13)/4

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

(x_1)=(−3+13)/4=10/4=5/2

(x_2)=(−3−13)/4=(−16)/4=−4

Final Answer

x=5/2,−4

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