(x+36)+(2x+12)+(1/3x+52)=180

Solution for (x+36)+(2x+12)+(1/3x+52)=180 equation:

(x+36)+(2x+12)+(1/3x+52)=180

We move all terms to the left:

(x+36)+(2x+12)+(1/3x+52)-(180)=0


Domain of the equation: 3x+52)!=0

x∈R


We get rid of parentheses

x+2x+1/3x+36+12+52-180=0

We multiply all the terms by the denominator


x*3x+2x*3x+36*3x+12*3x+52*3x-180*3x+1=0

Wy multiply elements

3x^2+6x^2+108x+36x+156x-540x+1=0

We add all the numbers together, and all the variables

9x^2-240x+1=0

a = 9; b = -240; c = +1;
Δ = b2-4ac
Δ = -2402-4·9·1
Δ = 57564
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:

$\sqrt{\Delta}=\sqrt{57564}=\sqrt{36*1599}=\sqrt{36}*\sqrt{1599}=6\sqrt{1599}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-6\sqrt{1599}}{2*9}=\frac{240-6\sqrt{1599}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+6\sqrt{1599}}{2*9}=\frac{240+6\sqrt{1599}}{18}
$