1/6x+1/2x+1/3=180

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

1/6x+1/2x+1/3=180

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


determiningTheFunctionDomain
1/6x+1/2x-180+1/3=0

We calculate fractions


24x^2/108x^2+18x/108x^2+54x/108x^2-180=0

We multiply all the terms by the denominator


24x^2+18x+54x-180*108x^2=0

We add all the numbers together, and all the variables

24x^2+72x-180*108x^2=0

Wy multiply elements

24x^2-19440x^2+72x=0

We add all the numbers together, and all the variables

-19416x^2+72x=0

a = -19416; b = 72; c = 0;
Δ = b2-4ac
Δ = 722-4·(-19416)·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72}{2*-19416}=\frac{-144}{-38832}
=3/809
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72}{2*-19416}=\frac{0}{-38832}
=0
$