x+6+2x-48+1/3x+42=180

Solution for x+6+2x-48+1/3x+42=180 equation:

x+6+2x-48+1/3x+42=180

We move all terms to the left:

x+6+2x-48+1/3x+42-(180)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/3x-180=0

We multiply all the terms by the denominator


3x*3x-180*3x+1=0

Wy multiply elements

9x^2-540x+1=0

a = 9; b = -540; c = +1;
Δ = b2-4ac
Δ = -5402-4·9·1
Δ = 291564
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:

$\sqrt{\Delta}=\sqrt{291564}=\sqrt{36*8099}=\sqrt{36}*\sqrt{8099}=6\sqrt{8099}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-6\sqrt{8099}}{2*9}=\frac{540-6\sqrt{8099}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+6\sqrt{8099}}{2*9}=\frac{540+6\sqrt{8099}}{18}
$