X-3/7=x/2x+1

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

X-3/7=X/2X+1

We move all terms to the left:

X-3/7-(X/2X+1)=0


Domain of the equation: 2X+1)!=0

X∈R


We get rid of parentheses

X-X/2X-1-3/7=0

We calculate fractions


X+(-7X)/14X+(-6X)/14X-1=0

We multiply all the terms by the denominator


X*14X+(-7X)+(-6X)-1*14X=0

Wy multiply elements

14X^2+(-7X)+(-6X)-14X=0

We get rid of parentheses

14X^2-7X-6X-14X=0

We add all the numbers together, and all the variables

14X^2-27X=0

a = 14; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·14·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*14}=\frac{0}{28}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*14}=\frac{54}{28}
=1+13/14
$