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

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

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

We move all terms to the left:

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


Domain of the equation: 3x+x-20+x-10+40)!=0

We move all terms containing x to the left, all other terms to the right

3x+x+x+40)!=30

x∈R


We add all the numbers together, and all the variables

-(2x+1/3x+10)+360=0

We get rid of parentheses

-2x-1/3x-10+360=0

We multiply all the terms by the denominator


-2x*3x-10*3x+360*3x-1=0

Wy multiply elements

-6x^2-30x+1080x-1=0

We add all the numbers together, and all the variables

-6x^2+1050x-1=0

a = -6; b = 1050; c = -1;
Δ = b2-4ac
Δ = 10502-4·(-6)·(-1)
Δ = 1102476
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:

$\sqrt{\Delta}=\sqrt{1102476}=\sqrt{4*275619}=\sqrt{4}*\sqrt{275619}=2\sqrt{275619}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1050)-2\sqrt{275619}}{2*-6}=\frac{-1050-2\sqrt{275619}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1050)+2\sqrt{275619}}{2*-6}=\frac{-1050+2\sqrt{275619}}{-12}
$