Solve for x

Question

2/x = x/3x+8

Answer 1

Since there is ambiguity in your posting, I will assume the +8 is in the denominator. i.e. x/(3x+8) vs (x/3x) + 8

 

Given: 2/x = x/(3x + 8)

 

Multiply both sides by (3x +8) to get rid of the right denominator

2(3x+8)/x = x

 

Multiply both sides by x to get rid of left denominator. Simplify numerator.

6x + 16 = x^2

 

Put everything on the same side. You will have a quadratic equation.

x^2 - 6x - 16 = 0

 

Factor. Double check by using FOIL to make sure you chose the right terms.

(x - 8)(x + 2) = 0

 

Break in two equations and solve for x

 

(x - 8) = 0

x = 8

 

(x + 2) = 0

x = -2

 

Therefore, x = 8 and x = -2