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^2-2205x+1=0

a = 15; b = -2205; c = +1;
Δ = b2-4ac
Δ = -22052-4·15·1
Δ = 4861965
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{-(-2205)-\sqrt{4861965}}{2*15}=\frac{2205-\sqrt{4861965}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2205)+\sqrt{4861965}}{2*15}=\frac{2205+\sqrt{4861965}}{30}
$