(x-30)+40+(x-10)+1/3x=360

Solution for (x-30)+40+(x-10)+1/3x=360 equation:

(x-30)+40+(x-10)+1/3x=360

We move all terms to the left:

(x-30)+40+(x-10)+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-30)+(x-10)+1/3x-320=0

We get rid of parentheses

x+x+1/3x-30-10-320=0

We multiply all the terms by the denominator


x*3x+x*3x-30*3x-10*3x-320*3x+1=0

Wy multiply elements

3x^2+3x^2-90x-30x-960x+1=0

We add all the numbers together, and all the variables

6x^2-1080x+1=0

a = 6; b = -1080; c = +1;
Δ = b2-4ac
Δ = -10802-4·6·1
Δ = 1166376
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:

$\sqrt{\Delta}=\sqrt{1166376}=\sqrt{4*291594}=\sqrt{4}*\sqrt{291594}=2\sqrt{291594}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1080)-2\sqrt{291594}}{2*6}=\frac{1080-2\sqrt{291594}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1080)+2\sqrt{291594}}{2*6}=\frac{1080+2\sqrt{291594}}{12}
$