(X/6)+5=(1/3)-x

Solution for (X/6)+5=(1/3)-x equation:

(X/6)+5=(1/3)-X

We move all terms to the left:

(X/6)+5-((1/3)-X)=0


Domain of the equation: 3)-X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

(+X/6)-((+1/3)-X)+5=0

We get rid of parentheses

X/6-((+1/3)-X)+5=0

We calculate fractions


3X^2/18X+()/18X+5=0

We multiply all the terms by the denominator


3X^2+5*18X+()=0

We add all the numbers together, and all the variables

3X^2+5*18X=0

Wy multiply elements

3X^2+90X=0

a = 3; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·3·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*3}=\frac{-180}{6}
=-30
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*3}=\frac{0}{6}
=0
$