x+(1/5x)+(x+48)=180

Solution for x+(1/5x)+(x+48)=180 equation:

x+(1/5x)+(x+48)=180

We move all terms to the left:

x+(1/5x)+(x+48)-(180)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+(+1/5x)+(x+48)-180=0

We get rid of parentheses

x+1/5x+x+48-180=0

We multiply all the terms by the denominator


x*5x+x*5x+48*5x-180*5x+1=0

Wy multiply elements

5x^2+5x^2+240x-900x+1=0

We add all the numbers together, and all the variables

10x^2-660x+1=0

a = 10; b = -660; c = +1;
Δ = b2-4ac
Δ = -6602-4·10·1
Δ = 435560
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:

$\sqrt{\Delta}=\sqrt{435560}=\sqrt{4*108890}=\sqrt{4}*\sqrt{108890}=2\sqrt{108890}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-660)-2\sqrt{108890}}{2*10}=\frac{660-2\sqrt{108890}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-660)+2\sqrt{108890}}{2*10}=\frac{660+2\sqrt{108890}}{20}
$