2/3x-1/3-3/4x=5/6

Solution for 2/3x-1/3-3/4x=5/6 equation:

2/3x-1/3-3/4x=5/6

We move all terms to the left:

2/3x-1/3-3/4x-(5/6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-3/4x-1/3-(+5/6)=0

We get rid of parentheses

2/3x-3/4x-1/3-5/6=0

We calculate fractions


(-720x^2)/648x^2+288x/648x^2+(-486x)/648x^2+(-144x)/648x^2=0

We multiply all the terms by the denominator


(-720x^2)+288x+(-486x)+(-144x)=0

We get rid of parentheses

-720x^2+288x-486x-144x=0

We add all the numbers together, and all the variables

-720x^2-342x=0

a = -720; b = -342; c = 0;
Δ = b2-4ac
Δ = -3422-4·(-720)·0
Δ = 116964
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{116964}=342$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-342)-342}{2*-720}=\frac{0}{-1440}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-342)+342}{2*-720}=\frac{684}{-1440}
=-19/40
$