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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


54x^2/72x^2+60x/72x^2+(-48x)/72x^2=0

We multiply all the terms by the denominator


54x^2+60x+(-48x)=0

We get rid of parentheses

54x^2+60x-48x=0

We add all the numbers together, and all the variables

54x^2+12x=0

a = 54; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·54·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*54}=\frac{-24}{108}
=-2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*54}=\frac{0}{108}
=0
$