(x+2)/14=(6/7)+(x-4)-3

Solution for (x+2)/14=(6/7)+(x-4)-3 equation:

(x+2)/14=(6/7)+(x-4)-3

We move all terms to the left:

(x+2)/14-((6/7)+(x-4)-3)=0


Domain of the equation: 7)+(x-4)-3)!=0

x∈R


We add all the numbers together, and all the variables

(x+2)/14-((+6/7)+(x-4)-3)=0

We calculate fractions


((x+2)*7)+x/98x+()/98x=0


We calculate terms in parentheses: +((x+2)*7), so:

(x+2)*7

We multiply parentheses

7x+14

Back to the equation:

+(7x+14)


We get rid of parentheses

7x+x/98x+()/98x+14=0

We multiply all the terms by the denominator


7x*98x+x+14*98x+()=0

We add all the numbers together, and all the variables

x+7x*98x+14*98x=0

Wy multiply elements

686x^2+x+1372x=0

We add all the numbers together, and all the variables

686x^2+1373x=0

a = 686; b = 1373; c = 0;
Δ = b2-4ac
Δ = 13732-4·686·0
Δ = 1885129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1885129}=1373$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1373)-1373}{2*686}=\frac{-2746}{1372}
=-2+1/686
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1373)+1373}{2*686}=\frac{0}{1372}
=0
$