(2/5x)+(x+30)+x+(3/5x)=180

Solution for (2/5x)+(x+30)+x+(3/5x)=180 equation:

(2/5x)+(x+30)+x+(3/5x)=180

We move all terms to the left:

(2/5x)+(x+30)+x+(3/5x)-(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

(+2/5x)+(x+30)+x+(+3/5x)-180=0

We add all the numbers together, and all the variables

x+(+2/5x)+(x+30)+(+3/5x)-180=0

We get rid of parentheses

x+2/5x+x+3/5x+30-180=0

We multiply all the terms by the denominator


x*5x+x*5x+30*5x-180*5x+2+3=0

We add all the numbers together, and all the variables

x*5x+x*5x+30*5x-180*5x+5=0

Wy multiply elements

5x^2+5x^2+150x-900x+5=0

We add all the numbers together, and all the variables

10x^2-750x+5=0

a = 10; b = -750; c = +5;
Δ = b2-4ac
Δ = -7502-4·10·5
Δ = 562300
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:

$\sqrt{\Delta}=\sqrt{562300}=\sqrt{100*5623}=\sqrt{100}*\sqrt{5623}=10\sqrt{5623}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-750)-10\sqrt{5623}}{2*10}=\frac{750-10\sqrt{5623}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-750)+10\sqrt{5623}}{2*10}=\frac{750+10\sqrt{5623}}{20}
$