X^2=6x / (5-x)

What is the sum of the roots of the above equation?

x = 3 or x = 2 or x = 0 thus: 5

Step-by-step explanation:

Solve for x over the real numbers:

x^2 = (6 x) / (5 - x)

Cross multiply:

x^2 (5 - x) = 6 x

Expand out terms of the left hand side:

5 x^2 - x^3 = 6 x

Subtract 6 x from both sides:

-x^3 + 5 x^2 - 6 x = 0

The left hand side factors into a product with four terms:

-x (x - 3) (x - 2) = 0

Multiply both sides by - 1:

x (x - 3) (x - 2) = 0

Split into three equations:

x - 3 = 0 or x - 2 = 0 or x = 0

Add 3 to both sides:

x = 3 or x - 2 = 0 or x = 0

Add 2 to both sides:

Answer: x = 3 or x = 2 or x = 0