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

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

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

We move all terms to the left:

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


Domain of the equation: 3x+12)!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

-2x-(1/3x+12)+360=0

We get rid of parentheses

-2x-1/3x-12+360=0

We multiply all the terms by the denominator


-2x*3x-12*3x+360*3x-1=0

Wy multiply elements

-6x^2-36x+1080x-1=0

We add all the numbers together, and all the variables

-6x^2+1044x-1=0

a = -6; b = 1044; c = -1;
Δ = b2-4ac
Δ = 10442-4·(-6)·(-1)
Δ = 1089912
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:

$\sqrt{\Delta}=\sqrt{1089912}=\sqrt{4*272478}=\sqrt{4}*\sqrt{272478}=2\sqrt{272478}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1044)-2\sqrt{272478}}{2*-6}=\frac{-1044-2\sqrt{272478}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1044)+2\sqrt{272478}}{2*-6}=\frac{-1044+2\sqrt{272478}}{-12}
$