(x/3)+(5/6)=(1/2)-x

Solution for (x/3)+(5/6)=(1/2)-x equation:

(x/3)+(5/6)=(1/2)-x

We move all terms to the left:

(x/3)+(5/6)-((1/2)-x)=0


Domain of the equation: 2)-x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+x/3)-((+1/2)-x)+(+5/6)=0

We get rid of parentheses

x/3-((+1/2)-x)+5/6=0

We calculate fractions


12x^2/36x+()/36x+60x/36x=0

We multiply all the terms by the denominator


12x^2+60x+()=0

We add all the numbers together, and all the variables

12x^2+60x=0

a = 12; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·12·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*12}=\frac{-120}{24}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*12}=\frac{0}{24}
=0
$