13/3x+1/2x=-1/6

Solution for 13/3x+1/2x=-1/6 equation:

13/3x+1/2x=-1/6

We move all terms to the left:

13/3x+1/2x-(-1/6)=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 get rid of parentheses

13/3x+1/2x+1/6=0

We calculate fractions


12x^2/216x^2+936x/216x^2+108x/216x^2=0

We multiply all the terms by the denominator


12x^2+936x+108x=0

We add all the numbers together, and all the variables

12x^2+1044x=0

a = 12; b = 1044; c = 0;
Δ = b2-4ac
Δ = 10442-4·12·0
Δ = 1089936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089936}=1044$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1044)-1044}{2*12}=\frac{-2088}{24}
=-87
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1044)+1044}{2*12}=\frac{0}{24}
=0
$