1/3x-11/6=5/4x

Solution for 1/3x-11/6=5/4x equation:

1/3x-11/6=5/4x

We move all terms to the left:

1/3x-11/6-(5/4x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(+5/4x)-11/6=0

We get rid of parentheses

1/3x-5/4x-11/6=0

We calculate fractions


(-528x^2)/432x^2+144x/432x^2+(-540x)/432x^2=0

We multiply all the terms by the denominator


(-528x^2)+144x+(-540x)=0

We get rid of parentheses

-528x^2+144x-540x=0

We add all the numbers together, and all the variables

-528x^2-396x=0

a = -528; b = -396; c = 0;
Δ = b2-4ac
Δ = -3962-4·(-528)·0
Δ = 156816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{156816}=396$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-396)-396}{2*-528}=\frac{0}{-1056}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-396)+396}{2*-528}=\frac{792}{-1056}
=-3/4
$