Solve Using the Quadratic Formula 4x^2-x-3=0

Problem

4*x2−x−3=0

Solution

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

a=4

b=−1

c=−3

2. Apply the formula for the quadratic equation x=(−b±√(,b2−4*a*c))/(2*a)

x=(−(−1)±√(,(−1)2−4*(4)*(−3)))/(2*(4))

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

x=(1±√(,1+48))/8

x=(1±√(,49))/8

4. Evaluate the square root.

x=(1±7)/8

5. Solve for both possible values of x

(x_1)=(1+7)/8=8/8=1

(x_2)=(1−7)/8=(−6)/8=−3/4

Final Answer

x=1,−3/4

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