x+1/5x+1/5x+x=180

Solution for x+1/5x+1/5x+x=180 equation:

x+1/5x+1/5x+x=180

We move all terms to the left:

x+1/5x+1/5x+x-(180)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/5x+1/5x-180=0

We multiply all the terms by the denominator


2x*5x-180*5x+1+1=0

We add all the numbers together, and all the variables

2x*5x-180*5x+2=0

Wy multiply elements

10x^2-900x+2=0

a = 10; b = -900; c = +2;
Δ = b2-4ac
Δ = -9002-4·10·2
Δ = 809920
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:

$\sqrt{\Delta}=\sqrt{809920}=\sqrt{64*12655}=\sqrt{64}*\sqrt{12655}=8\sqrt{12655}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-8\sqrt{12655}}{2*10}=\frac{900-8\sqrt{12655}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+8\sqrt{12655}}{2*10}=\frac{900+8\sqrt{12655}}{20}
$