1/3x+21/3-1/2x-1/2=-6

Solution for 1/3x+21/3-1/2x-1/2=-6 equation:

1/3x+21/3-1/2x-1/2=-6

We move all terms to the left:

1/3x+21/3-1/2x-1/2-(-6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-1/2x+13-1/2=0

We calculate fractions


8x/24x^2+(-3x)/24x^2+(-3x)/24x^2+13=0

We multiply all the terms by the denominator


8x+(-3x)+(-3x)+13*24x^2=0

Wy multiply elements

312x^2+8x+(-3x)+(-3x)=0

We get rid of parentheses

312x^2+8x-3x-3x=0

We add all the numbers together, and all the variables

312x^2+2x=0

a = 312; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·312·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*312}=\frac{-4}{624}
=-1/156
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*312}=\frac{0}{624}
=0
$