Solve for x (5x^2)/4=2(x-1)

Problem

(5*x2)/4=2*(x−1)

Solution

1. Eliminate the fraction by multiplying both sides of the equation by 4

5*x2=8*(x−1)

2. Distribute the 8 on the right side of the equation.

5*x2=8*x−8

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

5*x2−8*x+8=0

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

a=5

b=−8

c=8

5. Calculate the discriminant b2−4*a*c to determine the nature of the roots.

(−8)2−4*(5)*(8)=64−160

−96

6. Apply the quadratic formula using the negative discriminant, which indicates complex solutions.

x=(−(−8)±√(,−96))/(2*(5))

7. Simplify the radical using the imaginary unit i and factoring 96 as 16×6

√(,−96)=i√(,16⋅6)

√(,−96)=4*i√(,6)

8. Simplify the expression by dividing the terms in the numerator by the denominator.

x=(8±4*i√(,6))/10

x=(4±2*i√(,6))/5

Final Answer

(5*x2)/4=2*(x−1)⇒x=(4±2*i√(,6))/5

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