(x-20)+(x+10)+40+1/3x=360

Solution for (x-20)+(x+10)+40+1/3x=360 equation:

(x-20)+(x+10)+40+1/3x=360

We move all terms to the left:

(x-20)+(x+10)+40+1/3x-(360)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

(x-20)+(x+10)+1/3x-320=0

We get rid of parentheses

x+x+1/3x-20+10-320=0

We multiply all the terms by the denominator


x*3x+x*3x-20*3x+10*3x-320*3x+1=0

Wy multiply elements

3x^2+3x^2-60x+30x-960x+1=0

We add all the numbers together, and all the variables

6x^2-990x+1=0

a = 6; b = -990; c = +1;
Δ = b2-4ac
Δ = -9902-4·6·1
Δ = 980076
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:

$\sqrt{\Delta}=\sqrt{980076}=\sqrt{4*245019}=\sqrt{4}*\sqrt{245019}=2\sqrt{245019}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-990)-2\sqrt{245019}}{2*6}=\frac{990-2\sqrt{245019}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-990)+2\sqrt{245019}}{2*6}=\frac{990+2\sqrt{245019}}{12}
$