180=110+x+1/3x

Solution for 180=110+x+1/3x equation:

180=110+x+1/3x

We move all terms to the left:

180-(110+x+1/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(x+1/3x+110)+180=0

We get rid of parentheses

-x-1/3x-110+180=0

We multiply all the terms by the denominator


-x*3x-110*3x+180*3x-1=0

Wy multiply elements

-3x^2-330x+540x-1=0

We add all the numbers together, and all the variables

-3x^2+210x-1=0

a = -3; b = 210; c = -1;
Δ = b2-4ac
Δ = 2102-4·(-3)·(-1)
Δ = 44088
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:

$\sqrt{\Delta}=\sqrt{44088}=\sqrt{4*11022}=\sqrt{4}*\sqrt{11022}=2\sqrt{11022}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(210)-2\sqrt{11022}}{2*-3}=\frac{-210-2\sqrt{11022}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(210)+2\sqrt{11022}}{2*-3}=\frac{-210+2\sqrt{11022}}{-6}
$