5/6x+2/7-1/2x=4/63

Solution for 5/6x+2/7-1/2x=4/63 equation:

5/6x+2/7-1/2x=4/63

We move all terms to the left:

5/6x+2/7-1/2x-(4/63)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5/6x-1/2x+2/7-(+4/63)=0

We get rid of parentheses

5/6x-1/2x+2/7-4/63=0

We calculate fractions


(-672x^2)/37044x^2+3024x^2/37044x^2+30870x/37044x^2+(-18522x)/37044x^2=0

We multiply all the terms by the denominator


(-672x^2)+3024x^2+30870x+(-18522x)=0

We add all the numbers together, and all the variables

3024x^2+(-672x^2)+30870x+(-18522x)=0

We get rid of parentheses

3024x^2-672x^2+30870x-18522x=0

We add all the numbers together, and all the variables

2352x^2+12348x=0

a = 2352; b = 12348; c = 0;
Δ = b2-4ac
Δ = 123482-4·2352·0
Δ = 152473104
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{152473104}=12348$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12348)-12348}{2*2352}=\frac{-24696}{4704}
=-5+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12348)+12348}{2*2352}=\frac{0}{4704}
=0
$