X+3/7=x/2x

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

X+3/7=X/2X

We move all terms to the left:

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


Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

14X^2-1X=0

a = 14; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·14·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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