(2x+12)+(x+36)+(1/6x+56)=180

Solution for (2x+12)+(x+36)+(1/6x+56)=180 equation:

(2x+12)+(x+36)+(1/6x+56)=180

We move all terms to the left:

(2x+12)+(x+36)+(1/6x+56)-(180)=0


Domain of the equation: 6x+56)!=0

x∈R


We get rid of parentheses

2x+x+1/6x+12+36+56-180=0

We multiply all the terms by the denominator


2x*6x+x*6x+12*6x+36*6x+56*6x-180*6x+1=0

Wy multiply elements

12x^2+6x^2+72x+216x+336x-1080x+1=0

We add all the numbers together, and all the variables

18x^2-456x+1=0

a = 18; b = -456; c = +1;
Δ = b2-4ac
Δ = -4562-4·18·1
Δ = 207864
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:

$\sqrt{\Delta}=\sqrt{207864}=\sqrt{36*5774}=\sqrt{36}*\sqrt{5774}=6\sqrt{5774}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-456)-6\sqrt{5774}}{2*18}=\frac{456-6\sqrt{5774}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-456)+6\sqrt{5774}}{2*18}=\frac{456+6\sqrt{5774}}{36}
$