108=(x-6)(108/x+9)

Solution for 108=(x-6)(108/x+9) equation:

108=(x-6)(108/x+9)

We move all terms to the left:

108-((x-6)(108/x+9))=0


Domain of the equation: x+9))!=0

x∈R


We multiply parentheses ..

-((+108x^2+9x-648x-54))+108=0


We calculate terms in parentheses: -((+108x^2+9x-648x-54)), so:

(+108x^2+9x-648x-54)

We get rid of parentheses

108x^2+9x-648x-54

We add all the numbers together, and all the variables

108x^2-639x-54

Back to the equation:

-(108x^2-639x-54)


We get rid of parentheses

-108x^2+639x+54+108=0

We add all the numbers together, and all the variables

-108x^2+639x+162=0

a = -108; b = 639; c = +162;
Δ = b2-4ac
Δ = 6392-4·(-108)·162
Δ = 478305
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{478305}=\sqrt{81*5905}=\sqrt{81}*\sqrt{5905}=9\sqrt{5905}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(639)-9\sqrt{5905}}{2*-108}=\frac{-639-9\sqrt{5905}}{-216}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(639)+9\sqrt{5905}}{2*-108}=\frac{-639+9\sqrt{5905}}{-216}
$