X*(9-x)/x=2

Solution for X*(9-x)/x=2 equation:

X(9-X)/X=2

We move all terms to the left:

X(9-X)/X-(2)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X(-1X+9)/X-2=0

We multiply all the terms by the denominator


X(-1X+9)-2*X=0

We add all the numbers together, and all the variables

-2X+X(-1X+9)=0

We multiply parentheses

-1X^2-2X+9X=0

We add all the numbers together, and all the variables

-1X^2+7X=0

a = -1; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-1)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-1}=\frac{-14}{-2}
=+7
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-1}=\frac{0}{-2}
=0
$