Solve Using the Quadratic Formula 3x^2=8x-7

Problem

3*x2=8*x−7

Solution

1. Rearrange the equation into standard form a*x2+b*x+c=0 by subtracting 8*x and adding 7 to both sides.

3*x2−8*x+7=0

2. Identify the coefficients a b and c for use in the quadratic formula.

a=3

b=−8

c=7

3. State the quadratic formula.

x=(−b±√(,b2−4*a*c))/(2*a)

4. Substitute the values of a b and c into the formula.

x=(−(−8)±√(,(−8)2−4*(3)*(7)))/(2*(3))

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

x=(8±√(,64−84))/6

x=(8±√(,−20))/6

6. Simplify the square root using the imaginary unit i since the discriminant is negative.

√(,−20)=√(,−1⋅4⋅5)

√(,−20)=2*i√(,5)

7. Substitute the simplified radical back into the expression for x

x=(8±2*i√(,5))/6

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

x=(4±i√(,5))/3

Final Answer

x=(4±i√(,5))/3

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