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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


(-240x^2)/432x^2+144x/432x^2+(-324x)/432x^2=0

We multiply all the terms by the denominator


(-240x^2)+144x+(-324x)=0

We get rid of parentheses

-240x^2+144x-324x=0

We add all the numbers together, and all the variables

-240x^2-180x=0

a = -240; b = -180; c = 0;
Δ = b2-4ac
Δ = -1802-4·(-240)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-180}{2*-240}=\frac{0}{-480}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+180}{2*-240}=\frac{360}{-480}
=-3/4
$