10/3x+1/2x=-1/6

Solution for 10/3x+1/2x=-1/6 equation:

10/3x+1/2x=-1/6

We move all terms to the left:

10/3x+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

10/3x+1/2x+1/6=0

We calculate fractions


12x^2/216x^2+720x/216x^2+108x/216x^2=0

We multiply all the terms by the denominator


12x^2+720x+108x=0

We add all the numbers together, and all the variables

12x^2+828x=0

a = 12; b = 828; c = 0;
Δ = b2-4ac
Δ = 8282-4·12·0
Δ = 685584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{685584}=828$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(828)-828}{2*12}=\frac{-1656}{24}
=-69
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(828)+828}{2*12}=\frac{0}{24}
=0
$