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

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

(X-35)+X+(X-46)+1/5X=360

We move all terms to the left:

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


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We add all the numbers together, and all the variables

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

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}
$