3/7x-1=9/14x+3

Solution for 3/7x-1=9/14x+3 equation:

3/7x-1=9/14x+3

We move all terms to the left:

3/7x-1-(9/14x+3)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 14x+3)!=0

x∈R


We get rid of parentheses

3/7x-9/14x-3-1=0

We calculate fractions


42x/98x^2+(-63x)/98x^2-3-1=0

We add all the numbers together, and all the variables

42x/98x^2+(-63x)/98x^2-4=0

We multiply all the terms by the denominator


42x+(-63x)-4*98x^2=0

Wy multiply elements

-392x^2+42x+(-63x)=0

We get rid of parentheses

-392x^2+42x-63x=0

We add all the numbers together, and all the variables

-392x^2-21x=0

a = -392; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-392)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*-392}=\frac{0}{-784}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-392}=\frac{42}{-784}
=-3/56
$