1/2x+1/3-7=5/6x

Solution for 1/2x+1/3-7=5/6x equation:

1/2x+1/3-7=5/6x

We move all terms to the left:

1/2x+1/3-7-(5/6x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(+5/6x)-7+1/3=0

We get rid of parentheses

1/2x-5/6x-7+1/3=0

We calculate fractions


72x^2/108x^2+54x/108x^2+(-90x)/108x^2-7=0

We multiply all the terms by the denominator


72x^2+54x+(-90x)-7*108x^2=0

Wy multiply elements

72x^2-756x^2+54x+(-90x)=0

We get rid of parentheses

72x^2-756x^2+54x-90x=0

We add all the numbers together, and all the variables

-684x^2-36x=0

a = -684; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·(-684)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*-684}=\frac{0}{-1368}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*-684}=\frac{72}{-1368}
=-1/19
$