3x+1/12x+x=180

Solution for 3x+1/12x+x=180 equation:

3x+1/12x+x=180

We move all terms to the left:

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


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We add all the numbers together, and all the variables

4x+1/12x-180=0

We multiply all the terms by the denominator


4x*12x-180*12x+1=0

Wy multiply elements

48x^2-2160x+1=0

a = 48; b = -2160; c = +1;
Δ = b2-4ac
Δ = -21602-4·48·1
Δ = 4665408
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:

$\sqrt{\Delta}=\sqrt{4665408}=\sqrt{141376*33}=\sqrt{141376}*\sqrt{33}=376\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2160)-376\sqrt{33}}{2*48}=\frac{2160-376\sqrt{33}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2160)+376\sqrt{33}}{2*48}=\frac{2160+376\sqrt{33}}{96}
$