9x-108/x+36=0

Solution for 9x-108/x+36=0 equation:

9x-108/x+36=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


9x*x+36*x-108=0

We add all the numbers together, and all the variables

36x+9x*x-108=0

Wy multiply elements

9x^2+36x-108=0

a = 9; b = 36; c = -108;
Δ = b2-4ac
Δ = 362-4·9·(-108)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-72}{2*9}=\frac{-108}{18}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+72}{2*9}=\frac{36}{18}
=2
$