X+x+12+x+9/x=117

Solution for X+x+12+x+9/x=117 equation:

X+X+12+X+9/X=117

We move all terms to the left:

X+X+12+X+9/X-(117)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

3X+9/X-105=0

We multiply all the terms by the denominator


3X*X-105*X+9=0

We add all the numbers together, and all the variables

-105X+3X*X+9=0

Wy multiply elements

3X^2-105X+9=0

a = 3; b = -105; c = +9;
Δ = b2-4ac
Δ = -1052-4·3·9
Δ = 10917
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:

$\sqrt{\Delta}=\sqrt{10917}=\sqrt{9*1213}=\sqrt{9}*\sqrt{1213}=3\sqrt{1213}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-3\sqrt{1213}}{2*3}=\frac{105-3\sqrt{1213}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+3\sqrt{1213}}{2*3}=\frac{105+3\sqrt{1213}}{6}
$