(-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

We get rid of parentheses

-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
$