x+(x+35)+(x+46)+1/5x=360

Solution for x+(x+35)+(x+46)+1/5x=360 equation:

x+(x+35)+(x+46)+1/5x=360

We move all terms to the left:

x+(x+35)+(x+46)+1/5x-(360)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

x+x+x+1/5x+35+46-360=0

We multiply all the terms by the denominator


x*5x+x*5x+x*5x+35*5x+46*5x-360*5x+1=0

Wy multiply elements

5x^2+5x^2+5x^2+175x+230x-1800x+1=0

We add all the numbers together, and all the variables

15x^2-1395x+1=0

a = 15; b = -1395; c = +1;
Δ = b2-4ac
Δ = -13952-4·15·1
Δ = 1945965
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1395)-\sqrt{1945965}}{2*15}=\frac{1395-\sqrt{1945965}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1395)+\sqrt{1945965}}{2*15}=\frac{1395+\sqrt{1945965}}{30}
$