2/6x+1/3x=10

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

2/6x+1/3x=10

We move all terms to the left:

2/6x+1/3x-(10)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


6x/18x^2+6x/18x^2-10=0

We multiply all the terms by the denominator


6x+6x-10*18x^2=0

We add all the numbers together, and all the variables

12x-10*18x^2=0

Wy multiply elements

-180x^2+12x=0

a = -180; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-180)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-180}=\frac{-24}{-360}
=1/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-180}=\frac{0}{-360}
=0
$