x+1/9x+1/9x+x=180

Solution for x+1/9x+1/9x+x=180 equation:

x+1/9x+1/9x+x=180

We move all terms to the left:

x+1/9x+1/9x+x-(180)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/9x+1/9x-180=0

We multiply all the terms by the denominator


2x*9x-180*9x+1+1=0

We add all the numbers together, and all the variables

2x*9x-180*9x+2=0

Wy multiply elements

18x^2-1620x+2=0

a = 18; b = -1620; c = +2;
Δ = b2-4ac
Δ = -16202-4·18·2
Δ = 2624256
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:

$\sqrt{\Delta}=\sqrt{2624256}=\sqrt{2304*1139}=\sqrt{2304}*\sqrt{1139}=48\sqrt{1139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1620)-48\sqrt{1139}}{2*18}=\frac{1620-48\sqrt{1139}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1620)+48\sqrt{1139}}{2*18}=\frac{1620+48\sqrt{1139}}{36}
$