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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-36x^2)/432x^2+108x/432x^2+144x/432x^2=0

We multiply all the terms by the denominator


(-36x^2)+108x+144x=0

We add all the numbers together, and all the variables

(-36x^2)+252x=0

We get rid of parentheses

-36x^2+252x=0

a = -36; b = 252; c = 0;
Δ = b2-4ac
Δ = 2522-4·(-36)·0
Δ = 63504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63504}=252$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(252)-252}{2*-36}=\frac{-504}{-72}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+252}{2*-36}=\frac{0}{-72}
=0
$