1/7x-47/14=7/2x

Solution for 1/7x-47/14=7/2x equation:

1/7x-47/14=7/2x

We move all terms to the left:

1/7x-47/14-(7/2x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/7x-(+7/2x)-47/14=0

We get rid of parentheses

1/7x-7/2x-47/14=0

We calculate fractions


(-1316x^2)/196x^2+28x/196x^2+(-686x)/196x^2=0

We multiply all the terms by the denominator


(-1316x^2)+28x+(-686x)=0

We get rid of parentheses

-1316x^2+28x-686x=0

We add all the numbers together, and all the variables

-1316x^2-658x=0

a = -1316; b = -658; c = 0;
Δ = b2-4ac
Δ = -6582-4·(-1316)·0
Δ = 432964
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{432964}=658$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-658)-658}{2*-1316}=\frac{0}{-2632}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-658)+658}{2*-1316}=\frac{1316}{-2632}
=-1/2
$