x+1/3x+(x-9)=180

Solution for x+1/3x+(x-9)=180 equation:

x+1/3x+(x-9)=180

We move all terms to the left:

x+1/3x+(x-9)-(180)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

x+1/3x+x-9-180=0

We multiply all the terms by the denominator


x*3x+x*3x-9*3x-180*3x+1=0

Wy multiply elements

3x^2+3x^2-27x-540x+1=0

We add all the numbers together, and all the variables

6x^2-567x+1=0

a = 6; b = -567; c = +1;
Δ = b2-4ac
Δ = -5672-4·6·1
Δ = 321465
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-567)-\sqrt{321465}}{2*6}=\frac{567-\sqrt{321465}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-567)+\sqrt{321465}}{2*6}=\frac{567+\sqrt{321465}}{12}
$