4/3x+1/6x-11/12=1/3

Solution for 4/3x+1/6x-11/12=1/3 equation:

4/3x+1/6x-11/12=1/3

We move all terms to the left:

4/3x+1/6x-11/12-(1/3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

4/3x+1/6x-11/12-(+1/3)=0

We get rid of parentheses

4/3x+1/6x-11/12-1/3=0

We calculate fractions


(-3564x^2)/648x^2+288x/648x^2+108x/648x^2+(-72x)/648x^2=0

We multiply all the terms by the denominator


(-3564x^2)+288x+108x+(-72x)=0

We add all the numbers together, and all the variables

(-3564x^2)+396x+(-72x)=0

We get rid of parentheses

-3564x^2+396x-72x=0

We add all the numbers together, and all the variables

-3564x^2+324x=0

a = -3564; b = 324; c = 0;
Δ = b2-4ac
Δ = 3242-4·(-3564)·0
Δ = 104976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{104976}=324$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(324)-324}{2*-3564}=\frac{-648}{-7128}
=1/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(324)+324}{2*-3564}=\frac{0}{-7128}
=0
$