X-6+1/3x=180

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

X-6+1/3X=180

We move all terms to the left:

X-6+1/3X-(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

X+1/3X-186=0

We multiply all the terms by the denominator


X*3X-186*3X+1=0

Wy multiply elements

3X^2-558X+1=0

a = 3; b = -558; c = +1;
Δ = b2-4ac
Δ = -5582-4·3·1
Δ = 311352
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:

$\sqrt{\Delta}=\sqrt{311352}=\sqrt{4*77838}=\sqrt{4}*\sqrt{77838}=2\sqrt{77838}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-558)-2\sqrt{77838}}{2*3}=\frac{558-2\sqrt{77838}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-558)+2\sqrt{77838}}{2*3}=\frac{558+2\sqrt{77838}}{6}
$