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

Problem

(5*x2)/4=2*(x−2)

Solution

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

(5*x2)/4⋅4=2*(x−2)⋅4

5*x2=8*(x−2)

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

5*x2=8*x−16

3. Rearrange into standard form a*x2+b*x+c=0 by subtracting 8*x and adding 16 to both sides.

5*x2−8*x+16=0

4. Identify coefficients for the quadratic formula x=(−b±√(,b2−4*a*c))/(2*a) where a=5 b=−8 and c=16

x=(−(−8)±√(,(−8)2−4*(5)*(16)))/(2*(5))

5. Simplify the discriminant and the denominator.

x=(8±√(,64−320))/10

x=(8±√(,−256))/10

6. Simplify the square root using the imaginary unit i where √(,−256)=16*i

x=(8±16*i)/10

7. Reduce the fraction by dividing each term by the greatest common divisor, which is 2

x=(4±8*i)/5

Final Answer

(5*x2)/4=2*(x−2)⇒x=(4±8*i)/5

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