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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-54x^2)/72x^2+60x/72x^2+(-48x)/72x^2-1=0

We multiply all the terms by the denominator


(-54x^2)+60x+(-48x)-1*72x^2=0

Wy multiply elements

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

We get rid of parentheses

-54x^2-72x^2+60x-48x=0

We add all the numbers together, and all the variables

-126x^2+12x=0

a = -126; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-126)·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*-126}=\frac{-24}{-252}
=2/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-126}=\frac{0}{-252}
=0
$