1/6x+1/3x=1/4

Solution for 1/6x+1/3x=1/4 equation:

1/6x+1/3x=1/4

We move all terms to the left:

1/6x+1/3x-(1/4)=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 add all the numbers together, and all the variables

1/6x+1/3x-(+1/4)=0

We get rid of parentheses

1/6x+1/3x-1/4=0

We calculate fractions


(-54x^2)/288x^2+48x/288x^2+96x/288x^2=0

We multiply all the terms by the denominator


(-54x^2)+48x+96x=0

We add all the numbers together, and all the variables

(-54x^2)+144x=0

We get rid of parentheses

-54x^2+144x=0

a = -54; b = 144; c = 0;
Δ = b2-4ac
Δ = 1442-4·(-54)·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-144}{2*-54}=\frac{-288}{-108}
=2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+144}{2*-54}=\frac{0}{-108}
=0
$